Pricing and hedging in the presence of extraneous risks

• Published in: Stochastic processes and their applications Vol. 117; no. 6; pp. 742 - 765
• Main Authors: Dufresne, Pierre Collin, Hugonnier, Julien
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.06.2007; Elsevier Science; Elsevier
• Series: Stochastic Processes and their Applications
• Subjects: Event risk; Exact sciences and technology; Fair price; Incomplete markets; Mathematics; Nonmarket risks; Nonmarket risks Incomplete markets Utility based pricing Event risk Fair price; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Stochastic analysis; Stochastic processes; Utility based pricing; Event risk; 93E20; Fair price; Utility based pricing; 60H30; 91B38; Nonmarket risks; Incomplete markets; Almost sure convergence; Nonmarket risks; Incomplete markets; Utility based pricing; Event risk; Fair price; Necessary and sufficient condition; Price; 60H30; 91B38; 93E20; Pricing; Incomplete market; Financial market; Stochastic process; Application; Semimartingale
• ISSN: 0304-4149; 1879-209X
• DOI: 10.1016/j.spa.2006.10.004

Given an underlying complete financial market, we study contingent claims whose payoffs may depend on the occurrence of nonmarket events. We first investigate the almost-sure hedging of such claims. In particular, we obtain new representations of the hedging prices and provide necessary and sufficient conditions for a claim to be marketed. The analysis of various examples then leads us to investigate alternative pricing rules. We choose to embed the pricing problem into the agent’s portfolio decision and study reservation prices. We establish the existence and consistency of this pricing rule in a semimartingale model. We characterize the nonlinear dependence of the reservation price with respect to both the agent’s initial capital and the size of her position. The fair price arises as a limiting case.