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Maximizing the probability of a perfect hedge

Spivak, Gennady and Cvitanić, Jakša (1999) Maximizing the probability of a perfect hedge. Annals of Applied Probability, 9 (4). pp. 1303-1326. ISSN 1050-5164. http://resolver.caltech.edu/CaltechAUTHORS:SPIaap99

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Abstract

In the framework of continuous-time, Itô processes models for financial markets, we study the problem of maximizing the probability of an agent's wealth at time T being no less than the value C of a contingent claim with expiration time T. The solution to the problem has been known in the context of complete markets and recently also for incomplete markets; we rederive the complete markets solution using a powerful and simple duality method, developed in utility maximization literature. We then show how to modify this approach to solve the problem in a market with partial information, the one in which we have only a prior distribution on the vector of return rates of the risky assets. Finally, the same problem is solved in markets in which the wealth process of the agent has a nonlinear drift. These include the case of different borrowing and lending rates, as well as "large investor" models. We also provide a number of explicitly solved examples.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1214/aoap/1029962873DOIUNSPECIFIED
http://projecteuclid.org/euclid.aoap/1029962873PublisherUNSPECIFIED
Additional Information:1999 © Institute of Mathematical Statistics. Received July 1998; revised January 1999. Supported in part by NSF Grant DMS-95-03582. The results of this paper have been drawn from the first author’s [G.S.] doctoral dissertation at Columbia.
Funders:
Funding AgencyGrant Number
National Science FoundationDMS-95-03582
Subject Keywords:Hedging; partial information; large investor; margin requirements
Record Number:CaltechAUTHORS:SPIaap99
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:SPIaap99
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11672
Collection:CaltechAUTHORS
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Deposited On:18 Sep 2008 04:31
Last Modified:26 Dec 2012 10:17

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