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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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.
|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.|
|Subject Keywords:||Hedging; partial information; large investor; margin requirements|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Archive Administrator|
|Deposited On:||18 Sep 2008 04:31|
|Last Modified:||26 Dec 2012 10:17|
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