On utility-based super-replication prices of contingent claims with unbounded payoffs
| dc.creator | Oertel, Frank | |
| dc.creator | Owen, Mark | |
| dc.date | 2006-09-14 | |
| dc.date.accessioned | 2026-07-07T12:11:18Z | |
| dc.date.available | 2026-07-07T12:11:18Z | |
| dc.description | Consider a financial market in which an agent trades with utility-induced restrictions on wealth. For a utility function which satisfies the condition of reasonable asymptotic elasticity at $-\infty$ we prove that the utility-based super-replication price of an unbounded (but sufficiently integrable) contingent claim is equal to the supremum of its discounted expectations under pricing measures with finite {\it loss-entropy}. For an agent whose utility function is unbounded from above, the set of pricing measures with finite loss-entropy can be slightly larger than the set of pricing measures with finite entropy. Indeed, the former set is the closure of the latter under a suitable weak topology. Central to our proof is the representation of a cone $C_U$ of utility-based super-replicable contingent claims as the polar cone to the set of finite loss-entropy pricing measures. The cone $C_U$ is defined as the closure, under a relevant weak topology, of the cone of all (sufficiently integrable) contingent claims that can be dominated by a zero-financed terminal wealth. We investigate also the natural dual of this result and show that the polar cone to $C_U$ is generated by those separating measures with finite loss-entropy. The full two-sided polarity we achieve between measures and contingent claims yields an economic justification for the use of the cone $C_U$, and an open question. | |
| dc.identifier | https://arxiv.org/abs/math/0609403 | |
| dc.identifier | http://arxiv.org/abs/math/0609403 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210181 | |
| dc.subject | Probability | |
| dc.subject | Functional Analysis | |
| dc.subject | Optimization and Control | |
| dc.subject | Pricing of Securities | |
| dc.subject | 1B16, 46N10, 60G44 | |
| dc.title | On utility-based super-replication prices of contingent claims with unbounded payoffs | |
| dc.type | text |