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November 1999 Maximizing the probability of a perfect hedge
Jakša Cvitanić, Gennady Spivak
Ann. Appl. Probab. 9(4): 1303-1328 (November 1999). DOI: 10.1214/aoap/1029962873


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.


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Jakša Cvitanić. Gennady Spivak. "Maximizing the probability of a perfect hedge." Ann. Appl. Probab. 9 (4) 1303 - 1328, November 1999.


Published: November 1999
First available in Project Euclid: 21 August 2002

zbMATH: 0966.91042
MathSciNet: MR1728563
Digital Object Identifier: 10.1214/aoap/1029962873

Primary: 90A09 , 90A46
Secondary: 60H30 , 93E20

Keywords: hedging , large investor , margin requirements , partial information

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.9 • No. 4 • November 1999
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