Affirmed by published opinion. Judge KING wrote the opinion, in which Judge MICHAEL joined. Judge NIEMEYER wrote separately, concurring in part and dissenting in part and concurring in the judgment.
OPINION
KING, Circuit Judge:
On June 9, 2000, a shipment of aluminum that had travelled by sea from St. Petersburg, Russia, arrived at the Port of Baltimore, Maryland. The carrier (i.e., the owner of the ship) asserted a maritime lien against the cargo, and it subsequently filed in rem and in personam claims in the District of Maryland, seeking to recover unpaid freight. The shippers (i.e., the owners of the cargo), in turn, filed a counterclaim contesting the lien and seeking damages. The district court granted the carrier’s motions for summary judgment. The shippers have appealed, and as explained below, we affirm.
I.
Intamex, S.A., and Amaleo, A.G. (“Inta-mex and Amaleo” or the “Shippers”), are international metal traders. Both are incorporated in Switzerland and both are engaged primarily in the purchase and sale of aluminum. In the spring of 2000, Inta-mex and Amaleo bought aluminum in Russia for sale to American buyers. In order to have the aluminum transported to the United States, they booked ocean carriage aboard the M/V ANANGEL FIDELITY (the “FIDELITY”), a vessel owned by Hawkspere Shipping Company, Limited (“Hawkspere”), a Bahamian corporation.
Rather than contact Hawkspere directly to book passage for the aluminum, Inta-mex and Amaleo instead made the arrangements for ocean carriage through International Commodities Transport Services (“ICTS”), an Alabama corporation. ICTS is a “cargo consolidator”: it packages shipments bound for a common destination and charters a vessel to carry the cargo on behalf of various shippers. In the past, Intamex and Amaleo had arranged several shipments using ICTS, either directly or through their Russian agent, International Transportation Logistics (“ITL”). Generally, Intamex and Am-aleo would remit payment for the ocean freight charges to ICTS in Athens, Alabama. ICTS would then deduct its commissions and forward the balance to the carrier. There were occasions, however, when Intamex paid the ocean freight directly to the carrier, rather than by way of ICTS. It is undisputed that both Inta-mex and Amaleo were aware that ICTS did not use its own vessels for shipping, and that it instead brokered the services of other companies.
On April 28, 2000, ICTS, as charterer, entered into a voyage charterparty with Hawkspere, as owner, for the services of one of Hawkspere’s ships, the FIDELITY. A “voyage charterparty” is simply a contract for the hire of a ship. See William Tetley, Marine Cargo Claims 10 (3d ed.1988). The charterparty form employed in this instance was drafted in New York by the attorneys for ICTS, and it had been used in each of the approximately eight other charterparties that ICTS and Hawkspere had executed. In each instance, the form was modified with different details and rider terms, depending on the nature of the particular shipment. The terms of the charterparty for this shipment were negotiated through a Houston company, Argosy Shipping, and the charter was “fixed,” or made, in the United States. In addition to consolidating the cargo of Intamex and Amaleo for the St. [229]*229Petersburg to Baltimore voyage, ICTS also arranged for Hawkspere’s FIDELITY to carry cargo belonging to two other shippers.
Upon the loading of Intamex’s and Am-alco’s aluminum on board the FIDELITY, Hawkspere’s St. Petersburg agent issued ocean bills of lading for the cargo on pre-printed forms to Intamex and Amaleo, as shippers. A “bill of lading” is a contract for the carriage of goods by sea. See Tetley, Marne Cargo Claims 10 (3d ed.1988).1 The last of the bills of lading was issued on May 12, 2000, and all of the bills were immediately sent to Intamex and Amaleo. Once Intamex and Amaleo received the bills of lading, they were aware that the carrier of their cargo was Hawkspere. Both Intamex and Amaleo were also aware, prior to the shipment at issue, that payment of the ocean freight charges would ultimately have to be made to Hawkspere, the carrier of their cargo.
ICTS played no role in the preparation of the bills of lading, as the bills involved only Hawkspere, as carrier, and Intamex and Amaleo, as shippers. Conversely, In-tamex and Amaleo were in no way involved with the Hawkspere-ICTS charterparty.-In fact, prior to the initiation of this admiralty proceeding, neither Intamex nor Am-aleo ever saw a copy of the charterparty, nor were they otherwise aware of its terms. Moreover, neither shipper had any communication whatsoever with Hawk-spere prior to the June 2000 arrival of their cargo in Baltimore.
On the FIDELITY’S voyage from St. Petersburg to Baltimore, Intamex shipped 1767.19 metric tons of cargo, while Amaleo shipped 1233.06 metric tons. The Shippers admit that, as a result of this shipment, Intamex owed Hawkspere $54,782.89 in ocean freight, and Amaleo owed $38,224.86, for a total of $93,007.75. On May 16, 2000, Hawkspere sent its invoice to ICTS for all the ICTS-eonsolidat-ed cargo carried on the FIDELITY. ICTS, in turn, billed ITL (Intamex’s and Amalco’s Russian agent) for their cargoes at a rate that included not only the ocean freight of $31 per metric ton, but also stevedoring charges and ICTS’s commissions on the cargoes. ITL then billed Intamex and Amaleo, instructing them to remit the bulk of their payments directly to ICTS’s bank in Athens, Alabama, but also to wire $11,000 to ITL’s Russian bank, apparently in payment of ITL’s commission.
Instead of paying Hawkspere directly for the ocean freight that they owed, which Intamex has admitted was an option, Inta-mex and Amaleo claim to have paid their ocean freight in full to ICTS. Hawkspere, though, never received payment. According to the bills of lading, the ocean freight for the cargo was to have been paid four business days after signature on the bills of lading covering the cargo.2 The only monies that ICTS ever paid to Hawkspere [230]*230in connection with the FIDELITY voyage was a wire transfer of $12,000 made on May 30, 2000, and that wire transfer did not indicate whose ocean freight (Intamex, Amaleo, or the two other shippers whose cargos were also consolidated on the FIDELITY) was being paid. In order to avoid a dispute of material fact on .the issue of the sum that the Shippers still owed, Hawkspere stipulated to a $12,000 credit against the $93,007.75 total freight charges. It is therefore undisputed that Hawkspere never received ocean freight due for carriage of Intamex’s and Amalco’s cargo in the sum of $81,007.75.
The cargo of all shippers was discharged from the FIDELITY on or about June 9, 2000, at which time Hawkspere exercised its possessory maritime hen against the cargo shipped by Intamex and Amaleo on that vessel.3 After several weeks of negotiations between counsel for Hawkspere and counsel for Intamex and Amaleo, an agreement was reached where-under Hawkspere would arrest the cargo shipped by Intamex and Amaleo under bills of lading numbers 214 and 227 (the “Cargo”), and would release the remaining goods.4 Together, those two bills covered goods (specifically, sixty-five bundles of secondary aluminum and thirty-two pieces of aluminum alloy sows) whose value roughly equaled the amount of Hawk-spere’s claim against Intamex and Amaleo for unpaid ocean freight.
II.
On July 28, 2000, Hawkspere sued in admiralty and obtained a warrant to arrest the Cargo, in rem, pursuant to Supplemental Admiralty and Maritime Claims Rule C of the Federal Rules of Civil Procedure (“Supplemental Admiralty Rule C”). The United States Marshal carried out the arrest. On August 9, 2000, Intamex and Amaleo executed a letter of security, pursuant to which they placed the sum of $80,000 into the Registry of the Court, and the court released the Cargo from arrest. On September 11, 2000, Intamex and Am-aleo filed their Verified Answer and Claim to the Cargo, as well as a counterclaim against Hawkspere for wrongful arrest. On November 21, 2000, Intamex and Am-aleo brought a third party complaint against the cargo consolidator, ICTS, and its principal, Tony Gilbert.
On March 7, 2001, after discovery, Hawkspere moved for leave to amend its complaint to add Intamex and Amaleo as in personam defendants for breach of contract of carriage totaling $93,007.75, and to [231]*231increase to $93,007.75 the damages claimed in rem against the Cargo.5 On March 16, 2001, Hawkspere moved for partial summary judgment against the Cargo in rem under its original complaint and for summary judgment against Intamex and Am-aleo on their counterclaim. On April 2, 2001, Intamex and Amaleo filed a cross-motion for summary judgment on the original complaint and for partial summary judgment on their counterclaim. In their cross-motion, Intamex and Amaleo alleged for the first time that they were not the owners of the Cargo at the time of the arrest.
On May 22, 2001, the court issued a Memorandum Opinion and Order (1) granting Hawkspere’s motion for leave to amend; (2) granting Hawkspere’s motion for partial summary judgment on its original complaint against the Cargo, in rem, in the sum of $71,491.43 plus interest; (3) granting Hawkspere’s motion for summary judgment on Intamex’s and Amalco’s counterclaim; (4) denying Intamex’s and Amal-co’s cross-motion for summary judgment; and (5) denying Intamex’s and Amalco’s motion for partial summary judgment on their counterclaim. Hawkspere Shipping Co. Ltd. v. 65 Bundles of Secondary Aluminum, Mem. Op. & Order, Civ. No. S 00-2306 (D.Md. May 22, 2001) (the “Opinion”).
On May 23, 2001, Hawkspere filed its first amended complaint, adding Intamex and Amaleo as in personam defendants. Intamex and Amaleo answered the amended complaint on June 28, 2001, and added another (though virtually identical) counterclaim against Hawkspere. On August 30, 2001, Hawkspere moved for summary judgment on its amended complaint against the Cargo in rem and against Inta-mex and Amaleo in personam, and also moved to strike Intamex’s and Amalco’s new counterclaim. On September 19, 2001, Intamex and Amaleo filed a cross-motion for summary judgment on the amended complaint and a motion for partial summary judgment on their new counterclaim.
On October 2, 2001, the district court issued a Memorandum Opinion in which it both reiterated the findings contained in its May 22, 2001, Opinion, and determined that Intamex and Amaleo were liable to Hawkspere in personam for the unpaid ocean freight. Accordingly, the court entered an Order (1) granting Hawkspere summary judgment on the amended complaint in the sum of $81,007.75; (2) granting Hawkspere’s motion to strike Intamex and Amalco’s new counterclaim; (3) denying Intamex’s and Amalco’s cross-motion for summary judgment on the amended complaint; and (4) denying Intamex’s and Amalco’s motion for partial summary judgment on their new counterclaim. Hawkspere Shipping Co. Ltd. v. 65 Bundles of Secondary Aluminum, Mem. Op. & Order, Civ. No. S 00-2306 (D.Md. Oct. 2, 2001).
On October 16, 2001, Intamex and Amal-eo moved to alter or amend the court’s October 2, 2001, order, asking that prejudgment interest be set at the rate of 5.4%, that separate judgments be entered against Intamex and Amaleo, and that default judgments be entered against ICTS and Tony Gilbert on the third-party complaint. On October 30, 2001, the court issued an Order superseding that of October 2, 2001. In its Order of October 30, 2001, the court entered judgment in Hawk-spere’s favor on its in rem claim in the sum of $81,007.75, plus prejudgment interest of 6%. Judgment was also entered in Hawkspere’s favor on its in personam claims against Intamex, in the sum of [232]*232$47,714, and against Amaleo, in the sum of $33,293, both with prejudgment interest. Hawkspere Shipping Co. Ltd. v. 65 Bundles of Secondary Aluminum, Mem. Op. & Order, Civ. No. S 00-2306 (D.Md. Oct. 30, 2001).
On December 31, 2001, the court entered its final order, including judgment in favor of Intamex and Amaleo on their third party claims against ICTS and Tony Gilbert. Intamex and Amaleo filed a timely notice of appeal on January 7, 2002, and we possess jurisdiction pursuant to 28 U.S.C. § 1291.
III.
We review an award of summary judgment de novo, “viewing the facts and inferences drawn therefrom in the light most favorable to the non-movant.” Spriggs v. Diamond Auto Glass, 242 F.3d 179, 183 (4th Cir.2001). Summary judgment is appropriate when there is no genuine issue of material fact given the parties’ burdens of proof at trial. See Fed.R.Civ.P. 56(c); Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 247-48,106 S.Ct. 2505, 91 L.Ed.2d 202 (1986). There is a material dispute of fact when the fact’s existence or non-existence could lead a jury to different outcomes. Anderson, 477 U.S. at 248, 106 S.Ct. 2505.
IV.
Appellants Intamex and Amaleo contend that the district court erred in four primary respects: First, they assert that the law of England, and not that of the United States, governs this dispute. On this point rest the Shippers’ subsidiary contentions that the district court erred both in deciding that Hawkspere had a right of arrest in rem, and in dismissing Intamex’s and Ámalco’s wrongful arrest counterclaim. Second, Intamex and Amaleo contend that the court overlooked disputes of material fact regarding ICTS’s ostensible agency for receipt of ocean freight payments on Hawkspere’s behalf. Third, Intamex and Amaleo maintain that the court erred in deciding that they were estopped from proving that all Cargo had been sold before arrest. Fourth, and finally, Intamex and Amaleo assert that the court wrongly held them liable, in personam, to Hawk-spere, when the charterparty provided only for direct payments to Hawkspere by ICTS.
Addressing each in turn, the first question before us is whether the district court erred in ruling that this controversy is governed by the law of the United States. We hold that the court properly applied the law of this country, and thus that it also was correct both in deciding that Hawkspere had a right of arrest in rem, and in dismissing Intamex’s and Amalco’s wrongful arrest counterclaim.
A.
Intamex and Amaleo contend that English law governs Hawkspere’s rights with respect to the recovery of unpaid ocean freight, and that, pursuant to English law, there exists no right to assert a maritime lien against cargo, in rem, for unpaid freight. Thus, they maintain, because Supplemental Admiralty Rule C authorizes in rem actions only “[t]o enforce any maritime lien,” Fed.R.Civ.P. Supp. R. C(1)(A), Hawkspere wrongfully arrested their Cargo and is limited to seeking an in person-am remedy. See Interocean Shipping Co. v. M/V LYGARIA, 512 F.Supp. 960, 963 (D.Md.1981) (“Claims otherwise maritime in nature, but not giving rise to a [maritime] lien, must be pursued in person-am.”). Hawkspere, by contrast, insists that this dispute is governed by United States law, under which it is not limited to an in personam remedy, but which instead entitles it to seize cargo to secure pay[233]*233ment. See The Bird of Paradise, 72 U.S. (5 Wall.) 545, 554, 18 L.Ed. 662 (1866). Hawkspere contends that, under United States law, it was entitled to arrest the Cargo.
Intamex and Amaleo maintain that English law applies because the charterparty between Hawkspere and ICTS contained a “Law and Arbitration” clause, which provided that the charterparty itself was to be governed by and construed in accordance with English law. Hawkspere’s response is two-fold: First, it contends that the choice-of-law clause in the charterparty is inapplicable since (a) the charterparty is a contract to which Intamex and Amaleo are not parties, and (b) the charterparty’s terms were not successfully incorporated into the bills of lading. Second, Hawk-spere maintains that, even if successfully incorporated, the charterparty’s choice of law provisions are ambiguous. Either way, Hawkspere contends, there is no valid contractual choice of law, and the applicable analysis is that set forth in Lauritzen v. Larsen, 345 U.S. 571, 73 S.Ct. 921, 97 L.Ed. 1254 (1953). Under Lauritzen, according to Hawkspere, United States law governs.
B.
“[W]here the parties specify in their contractual agreement which law will apply, admiralty courts will generally give effect to that choice.” Chan v. Soc’y Expeditions, Inc., 123 F.3d 1287, 1297 (9th Cir.1997) (enforcing choice-of-law clause in marine passenger ticket). “In the absence of a contractual choice-of-law clause, federal courts sitting in admiralty apply federal maritime choice-of-law principles derived from the Supreme Court’s decision in Lau-ritzen ... and its progeny.” Id.; see Sundance Cruises Corp. v. The Am. Bureau of Shipping, 7 F.3d 1077, 1081 (2d Cir.1993); see also The Bremen v. Zapata Off-Shore Co., 407 U.S. 1, 92 S.Ct. 1907, 32 L.Ed.2d 513 (1972) (holding that courts should enforce a choice-of-law clause when it is part of a “freely negotiated private international agreement”); Richards v. Lloyd’s of London, 135 F.3d 1289, 1292-93 (9th Cir.1998) (same).
The contractual agreement at issue here is that contained in the bills of lading — the contracts between carrier Hawk-spere and shippers Intamex and Amaleo for carriage of goods. While the bills themselves contain no choice-of-law clause, they do purport to incorporate “[a]ll terms and conditions, liberties and exceptions of the CharterParty” —the contract between carrier Hawkspere and cargo consolidator ICTS for hire of a ship. And the charterparty, in turn, states that it “shall be governed by and construed in accordance with English law.”
Quoting the provisions of the charterparty, Intamex and Amaleo contend that English, not United States, law governs: the charterparty between Hawkspere and ICTS, they insist, was effectively incorporated into the bills of lading between Hawkspere and themselves. As Hawkspere notes, though, the incorporation is imperfect, in that while the bills of lading state that they are “to be used with charter-parties,” the spaces provided for insertion of the date of the governing charterparty are left blank. Hawkspere contends that, absent specific identification of the charterparty, its terms are not effectively incorporated into the bills of lading.
Courts consistently hold that attempts to incorporate a charterparty into a bill of lading are ineffective when the spaces in the bill that would have identi[234]*234fied the charterparty are left blank.6 See 2A Benedict on Admiralty § 184 at 17-62 (7th ed.2002) (citing cases). Decisions in which courts have found a proper incorporation are those in which the charterparty was identified in the bill of lading, at the least, by date. See, e.g., Steel Warehouse, 141 F.3d at 237. Identification is particularly important when, as here, there are multiple charter agreements between the same parties simultaneously. See id. In this case, the date of the charterparty was not included in the bills of lading. In fact, the bills contained no reference whatsoever to the relevant, April 28, 2000, charterparty, and Intamex and Amaleo were provided no effective notice of the charterparty’s terms. Under the circumstances, we cannot say that there was a successful incorporation of that document’s terms. Thus, we agree with Hawkspere that the charterparty cannot resolve for us the question of whether the law of England or that of the United States governs this dispute.
C.
Lacking a valid contractual choice of law, we turn to the choice-of-law analysis provided by the Supreme Court in Lauritzen v. Larsen, 345 U.S. 571, 73 S.Ct. 921, 97 L.Ed. 1254 (1953). See Cardinal Shipping v. M/S Seisho Maru, 744 F.2d 461, 464-66 (5th Cir.1984) (applying Lauritzen principles in context of contractually derived maritime lien). Under Lauritzen, a court must consider seven factors in determining the governing law for a particular dispute: (1) the place of the wrongful act, if any; (2) the law of the flag; (3) the domicile of the plaintiff; (4) the domicile of the shipowner; (5) the place of the contract; (6) the inaccessibility of a foreign forum; and (7) the law of the forum. 345 U.S. at 583-92, 73 S.Ct. 921. One of the causes of action asserted by Intamex and Amaleo is wrongful arrest of the Cargo; and the arrest of the Cargo clearly occurred in the United States. The law of the flag is unknown and not part of the record. The domicile of the plaintiffs, In-tamex and Amaleo, is Switzerland. The domicile of the shipowner, Hawkspere, is the Bahamas. The place of contracting is Russia, where the bills of lading were signed. And the forum is in the United States, which has the advantage of convenience at least to Hawkspere. Given, as well, that ICTS is an American corporation; that the charterparty was drafted in New York and negotiated through a broker in Houston; that the goods were shipped to and seized in Baltimore; that Intamex and Amaleo had substantial and ongoing ties with the United States; and that the only contact with England is a choice-of-law clause in a charterparty that simultaneously attempts (by way of its USA Paramount provision) to select the law of the United States, the district court did not err in holding that the United States has a stronger connection to this dispute than any other country, and that its law governs.
D.
Under United States law, a maritime lien arises for freight due from the cargo owner, The Bird of Paradise, 72 U.S. at 554, and, as Intamex and Amaleo concede, United States law permits an action in rem “[t]o enforce any maritime lien,” Supp. R. C(1)(A). Because the district court correctly concluded that this dispute is governed by the law of the United States, it follows that it was also [235]*235correct in holding both that Hawkspere had a right of arrest in rem, and in dismissing Intamex’s and Amalco’s wrongful arrest counterclaim.
V.
Intamex and Amaleo next assert that the district court overlooked substantial disputes of material fact concerning ICTS’s status as Hawkspere’s “ostensible” or “apparent” agent. They principally contend that, under English law (which they insist governs the case), ICTS was Hawkspere’s ostensible agent because “Hawkspere always looked to ICTS to collect payment for it.” Appellants’ Br. at 19. According to Intamex and Amaleo, they “each reasonably believed that ICTS was acting for Hawkspere and relied on that.” Id. at 20. Unlike United States law, which emphasizes the principal’s overt and direct representations in cases of apparent authority, English law, they assert, “looks at the course of dealing, and the position in which the principal has placed the agent, asking generally, which party was in the better position of preventing the loss.” Appellants’ Br. at 23. Under this standard, they maintain, ICTS should be viewed as Hawkspere’s agent, and the Shippers’ payment to ICTS should discharge their obligation to pay Hawkspere.
The district court rejected this ostensible agency argument on the ground that it was maintainable only under English law, which did not apply. Opinion at 229-30. The court held that the applicable United States rule was that, “where a shipper chooses to pay a [cargo consolidator] who does not remit the payment to the ocean carrier, the shipper assumes the risk that the [consolidator] might not pay the freight to the carrier, and the shipper’s duty to pay freight is not discharged, absent evidence that the [consolidator] was acting as the agent of the carrier.” Id. at 2. The court then noted that agency can be established, under United States law, only by evidence of overt acts on the part of the principal that would indicate an agency relationship; the subjective beliefs of the persons dealing with the alleged agent are thus irrelevant to the inquiry. Id. at 5. Applying this rule of agency, the court concluded that there was insufficient evidence to create a triable issue of fact regarding whether ICTS was acting as Hawkspere’s agent when it accepted payment from Intamex and Amaleo. Id. at 4-5.-
As the district court properly recognized, were ICTS the agent of Hawkspere, then Intamex’s and Amalco’s remission of payment to ICTS would relieve them of liability under the bills of lading. See Strachan Shipping Co. v. Dresser, Indus., 701 F.2d 483, 486-87 (5th Cir.1983). The court, however, concluded that Intamex and Amaleo had failed to proffer the requisite overt acts on the part of the purported principal, Hawkspere, that would indicate an agency relationship. We agree.
Intamex and Amaleo, as the parties asserting the existence of a principal-agent relationship between Hawkspere and ICTS, have the burden of proof on this issue. See McLean Contracting Co. v. Waterman S.S. Carp., 277 F.3d 477, 479 (4th Cir.2002). Since it appears to be undisputed that ICTS never had actual authority to act as Hawkspere’s collection agent, Intamex and Amaleo are presumably contending that we should construe ICTS’s relationship with Hawkspere as one of apparent agency. To prove apparent agency, they would need to show that Hawkspere held out ICTS as authorized to [236]*236act on its behalf. See Crothers v. Commodity Futures Trading Comm., 33 F.3d 405, 410 (4th Cir.1994).
The evidence of agency that the Shippers proffer is thin, to say the least. Inta-mex and Amaleo first note that Hawkspere “always looked to ICTS to collect payment for it.” Appellants’ Br. at 19. That Hawkspere did so, though, demonstrates nothing more remarkable than the fact that the fielding of payments was one of the services that ICTS chose to provide to the shippers for whom it consolidated. Its provision of that service in no way indicates that it was acting as Hawkspere’s collection agent. See Strachan Shipping Co., 701 F.2d at 486 (refusing to infer agency from fact that carrier initially directed its collection efforts to cargo consolidator). The Shippers next point out that they both “presented unrefuted testimony, that each reasonably believed that ICTS was acting for Hawkspere and relied on that.” Appellants’ Br. at 20. Under United States law, however, the Shippers’ subjective beliefs are irrelevant to the inquiry; only evidence of Hawkspere’s conduct can prove agency. See Overnite Transp. Co. v. NLRB, 140 F.3d 259, 266-67 (D.C.Cir.1998) (holding that agency is provable only by principal’s conduct, and not by subjective beliefs of those dealing with alleged agent); Auvil v. Grafton Homes, 92 F.3d 226, 230 (4th Cir.1996) (“An agent’s authority must be conferred by some manifestation by the principal that the agent is authorized to act on the principal’s behalf.” (emphasis in original)). Finally, In-tamex and Amaleo observe that the evidence indicated that Hawkspere paid ICTS no commission on the freight that ICTS collected for Hawkspere. Appellants’ Br. at 20. This fact, though, cuts directly against agency, since it indicates that Hawkspere and ICTS lacked any formal relationship at all. On this record, the court was correct to conclude that there was no triable issue of fact as to whether ICTS acted as an actual or apparent agent for Hawkspere when it accepted payment from Intamex and Amaleo.
VI.
Given that ICTS was not Hawkspere’s agent, it remains only to be determined whether there exists any other basis on which the Shippers might be excused from their liability to pay Hawkspere the freight that is due under the bills of lading. In this respect, it is worth noting that no party to this dispute has done other than what it was expected to do: Hawkspere carried the goods, and Intamex and Amal-eo tendered payment of freight. The trouble arises from the fact that the Shippers sent their payments not to Hawkspere directly, but rather by way of the consolidator, ICTS, who apparently then failed to forward the money on to its intended destination. Thus, the question: should Inta-mex and Amaleo have to pay twice, or should Hawkspere instead receive no payment at all?
There exists a split among the circuits on the question of which party, the shipper or the carrier, bears the risk that the cargo consolidator might, as here, fail to forward the freight payment to the carrier. Under the semi-strict “assumption of risk” view — the view taken by the district court — a shipper remains liable to a carrier, regardless of the shipper’s payment to a cargo consolidator like ICTS, unless the carrier intentionally released the shipper from its duty to pay under the bill of lading. See Nat’l Shipping Co. of Saudi Arabia v. Omni Lines, 106 F.3d 1544, 1546-47 (11th Cir.1997) (adopting rule of “semi-strict liability for shippers,” such that “unless the carrier intends to release the shipper from its duty to pay under the bill of lading, the shipper remains liable to [237]*237the carrier, irrespective of the shipper’s payment to a [cargo consolidator]”); Strachan Shipping Co., 701 F.2d at 489-90 (holding that shipper is relieved of liability only if it can demonstrate that carrier actually released it); Sectr-Land Serv. v. Amstar Corp., 690 F.Supp. 246 (S.D.N.Y.1988). Taking this approach, only if the carrier has released the shipper from liability under the bills of lading is the shipper discharged from his duty to pay the carrier by remitting payment to the consolidator; otherwise, the shipper, by choosing not to pay the carrier directly, assumes the risk that the consolidator might fail to forward the freight payment on to the carrier.
Under an alternative, “equitable estop-pel” view, when a shipper pays freight to a consolidator and the consolidator subsequently fails to forward the payment on to the carrier, the shipper does not remain hable to the carrier, so long as the circumstances indicate that the carrier led the shipper to believe that payment to the cargo consolidator would discharge the debt.7 See Olson Distrib. Sys. v. Glaswrit Am., 850 F.2d 295 (6th Cir.1988) (holding doctrine of equitable estoppel barred carrier’s claim against shipper for payment of freight bills, after carrier’s documents and dilatory conduct led shipper to believe that carrier was receiving freight payments from cargo consolidator); Inman Freight Sys., Inc. v. Olin Corp., 807 F.2d 117, 121 (8th Cir.1986) (holding that carrier may be estopped from collecting freight charges from shipper who paid freight to consolidator in reliance on carrier’s representation that such payment would discharge shipper’s bill of lading obligation); Mediterranean Shipping Co. v. Elof Hansson, Inc., 693 F.Supp. 80, 84 (S.D.N.Y.1988) (holding that carrier is estopped from collecting freight charges from shipper when shipper had paid consolidator in reliance on carrier’s misrepresentation that it had already received its payment from consolidator, and shipper would thus otherwise be unjustifiably liable for double payment). Thus, under the approach taken by the Sixth and Eighth Circuits, a shipper need not demonstrate that the carrier actually released it from its duty of payment in order to escape liability; rather, the shipper needs merely to show that the carrier’s actions would have led a reasonable shipper in his position to believe itself to be released.
This issue appears to be one of first impression in this circuit, and we here adopt the assumption of risk approach. Shippers such as Intamex and Amaleo can always avoid the loss by simply paying their carrier directly. When, as here, they choose not to do so, it is they who appropriately bear the risk that such a choice creates. As the Eleventh Circuit explained, “the bill of lading is a contract between the shipper and the carrier and the carrier has a contractual right to expect payment pursuant to that bill. Should the shipper wish to avoid liability for double payment, it must take precaution to deal with a reputable [cargo consolidator] or contract with the carrier to secure its release.” Nat’l Shipping Co., 106 F.3d at 1547. The Eleventh Circuit also quoted with approval the reasoning of the Fifth Circuit:
[238]*238[W]e think that our result comports with economic reality. A [cargo consolidator] provides a service. He sells his expertise and experience in booking and preparing cargo for shipment. He depends upon the fees paid by both shipper and carrier. He has few assets, and he books amounts of cargo far exceeding his net worth. Carriers must expect payment will come from the shipper, although it may pass through the forwarder’s hands. While the carrier may extend credit to the forwarder, there is no economically rational motive for the carrier to release the shipper. The more parties that are liable, the greater the assurance for the carrier that he will be paid.
Id. (quoting Strachan Shipping Co., 701 F.2d at 490). We find this reasoning persuasive and conclude that, where a shipper chooses to remit payment by way of a cargo consolidator, rather than directly to the ocean carrier, the shipper assumes the risk that the consolidator might not forward the freight payment to the carrier. The shipper’s duty to pay freight is not discharged, absent evidence that the carrier has actually released the shipper from its duty to pay under the bill of lading. Because Intamex and Amaleo have offered no evidence that Hawkspere in fact released them from liability, the district court was correct to hold the Shippers remained liable for the ocean freight charges.
VII.
Shippers Intamex and Amaleo next contend that the district court erred in applying equitable estoppel to bar them from denying ownership of the Cargo. The Shippers asserted below that, even if United States law applies, there was no valid maritime lien, since they had sold the Cargo before Hawkspere’s hen attached. The court rejected this contention, holding that the Shippers were estopped from denying ownership, since they had previously claimed the Cargo. Accordingly, the court denied both the Shippers’ cross-motion for summary judgment on Hawkspere’s in rem claims, and their motion for partial summary judgment on their counterclaim for wrongful arrest.
The Shippers contend that the court erred in failing to make a specific finding that Hawkspere relied to its detriment on any misrepresentation by Intamex and Amaleo as to the ownership of the Cargo. See Carneiro Da Cunha v. Standard Fire Ins. Co., 129 F.3d 581, 587 (11th Cir.1997) (stating that detrimental reliance on misrepresentation is required element of equitable estoppel under federal common law); Marine Transp. Servs. v. Python High Performance Marine Corp., 16 F.3d 1133, 1139 & n. 8 (11th Cir.1994) (same, and noting that federal common law of estoppel applies in cases arising under admiralty jurisdiction). They assert that it was Hawkspere’s obligation to inquire into the ownership of the Cargo before asserting its hen, rather than Intamex’s and Amal-co’s obligation to disclose their lack of ownership. Appellants’ Br. at 26-29.
Hawkspere responds that it was the obligation of the Shippers to disclose their alleged non-ownership. Hawkspere claims that it relied to its detriment on the Shippers’ de facto misrepresentation of ownership in litigation strategy and discovery, when it proceeded on the assumption that there was no issue regarding ownership. Intamex and Amaleo, Hawkspere contends, engaged in misconduct when they faded to disclose their lack of ownership, and they should not be permitted to benefit from that misconduct.
Under the doctrine of equitable estoppel, a party is precluded from asserting rights he otherwise would have had [239]*239against another when his own conduct renders assertion of those rights contrary to equity. Int’l Paper Co. v. Schwabedissen Maschinen, 206 F.3d 411, 417-18 (4th Cir.2000). Here, Hawkspere asserted its pos-sessory maritime lien on June 9, 2000, and it obtained a warrant for the Cargo’s arrest on July 28, 2000. Until they filed their cross-motion for summary judgment on April 2, 2001, Intamex and Amaleo failed to disclose that the Cargo carried under bills of lading 214 and 227 allegedly was sold to third parties prior to the notice of hen. By that point, they had bypassed multiple opportunities to inform Hawk-spere (and, later, the court) of the purported change in ownership, including: (1) in response to Hawkspere’s June 2000 written notice of the claimed lien; (2) during their several weeks of negotiation with Hawkspere over which cargo would be arrested; (3) in a post-arrest judicial proceeding that they could have requested (but did not request) under Supplemental Admiralty Rule E(4) to contest the validity of the arrest; (4) in their September 2000 Answer, Counterclaim, and Claim to the Cargo; and (5) throughout the extended discovery proceedings. Despite these numerous opportunities, the Shippers said nothing about a defense of non-ownership. In fact, they remained silent even though Supplemental Admiralty Rule C(6), applicable at all relevant times, specifically required them to state, in their Claim to the Cargo, the specific interest in the Cargo “by which the claimant demands restitution.” Furthermore, on August 9, 2000, counsel for Intamex and Amaleo issued a letter of security to Hawkspere in which they stated “[i]n consideration for your releasing to our clients Intamex and Amal-eo or their designates, certain Intamex and Amaleo cargo ” (emphasis added). And it was Intamex and Amaleo who posted the security for the Cargo’s release.
The Shippers had a duty under Supplemental Admiralty Rule C to disclose the alleged non-ownership of the Cargo. Their silence on the point thus effectively constituted a material misrepresentation. See Edell & Assoc., P.C. v. Law Offices of Peter Angelos, 264 F.3d 424, 440 (4th Cir.2001) (holding that silence can constitute misrepresentation when there is duty to speak). Furthermore, the statement in their August 9, 2000, letter to Hawkspere amounts to an affirmative misrepresentation. Finally, the Shippers undoubtedly slept on their right to assert non-ownership by failing for so long, and despite so many opportunities, to assert that defense; they have proffered no exculpatory explanation for their failure (in fact, Intamex and Amaleo admit that they “knew all along that they had sold the [Cjargo,” Appellants’ Br. at 26). Lacking any reason to believe that ownership was in question, Hawkspere was entitled to and did proceed in this litigation on the assumption that the Cargo remained the property of the Shippers. In light of Intamex’s and Amalco’s misrepresentations and their dilatory assertion of non-ownership, the court did not err in applying equitable estoppel when the Shippers eventually sought, in their cross-motion for summary judgment, to assert non-ownership.
VIII.
Lastly, Intamex and Amaleo contend that the district court erred when it held, contrary to the charterparty, that they owed Hawkspere direct payments, in per-sonam, under the bills of lading. They point out that the bills of lading provide that “All terms and conditions, liberties of the Charter Party, dated as overleaf, including the Law and Arbitration Clause, are herewith incorporated”; and the char-terparty states that a charterer will be responsible for freight charges “only to such extent as the [carrier] ha[s] been [240]*240unable to obtain payment thereof by exercising the lien on the [C]argo.” The Shippers interpret this clause to mean that, under the charterparty (as incorporated into the bills of lading), Hawkspere’s only remedy against Intamex and Amaleo is in rem.
However, as explained in Part IV.B, swpra, the bills of lading did not in fact successfully incorporate the terms of the charterparty; and the bills of lading, as contracts that obligate the Shippers directly to Hawkspere, clearly support an in personam action. See 2 Thomas J. Schoenbaum, Admiralty and Maritime Law § 10-11 (3d ed.2001) (explaining that a bill of lading is a “memorandum of the contract ... concluded between the carrier and the shipper ” (emphasis added)). Under the provisions of Supplemental Admiralty Rule C, such an in personam action is properly combined with a suit in rem. Fed. R. Civ. P. Supp. R. C(l) (“[A] party who may proceed in rem may also, or in the alternative, proceed in personam against any person who may be liable.”). Thus, the court was correct in determining that Hawkspere was entitled to pursue the Shippers in personam for payment of freight.
IX.
For the foregoing reasons, the judgment of the district court is affirmed.
AFFIRMED