Variational Equality and Portfolio Optimization for Price Processes with Jumps

Hiroshi Kunita
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Hiroshi Kunita: Department of Mathematical Science, Nanzan University, Seirei-cho, Seto, 489-0863, Japan

Chapter 9 in Stochastic Processes and Applications to Mathematical Finance, 2004, pp 167-194 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractWe study the optimization of the portfolio/consumption which maximizes the expected value of utilities in the case where the price process has jumps, i.e., the solution of a SDE driven by a Lévy process. A duality method is taken. There are infinitely many equivalent martingale measures (or state price densities). Among them we find an optimal state price density, with respect to which the optimal contingent claim is attainable. For the proof, a useful variational equality is introduced.

Keywords: Stochastic Processes; Stochastic Differential Equations; Malliavin Calculus; Stochastic Control and Optimization; Functionals of Brownian Motions and Lévy Processes; Stochastic Models of Financial Market; Derivative Pricing; Hedging Problem (search for similar items in EconPapers)
Date: 2004
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