The Annals of Applied Probability

Maximizing the probability of a perfect hedge

Jakša Cvitanić and Gennady Spivak

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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.

Article information

Ann. Appl. Probab., Volume 9, Number 4 (1999), 1303-1328.

First available in Project Euclid: 21 August 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 90A09 90A46
Secondary: 93E20: Optimal stochastic control 60H30: Applications of stochastic analysis (to PDE, etc.)

Hedging partial information large investor margin requirements


Spivak, Gennady; Cvitanić, Jakša. Maximizing the probability of a perfect hedge. Ann. Appl. Probab. 9 (1999), no. 4, 1303--1328. doi:10.1214/aoap/1029962873.

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