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2002•The Annals of Applied ProbabilityOpen access

Utility based optimal hedging in incomplete markets

Mark P. Owen

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Abstract

We provide the solution to a fusion of two fundamental problems in mathematical finance. The first problem is that of maximizing the expected utility of terminal wealth of an investor who holds a short position in a contingent claim, and the second is that of maximizing terminal wealth where the utility function allows the investor to have negative wealth. Under assumptions of reasonable asymptotic elasticity on the investor's utility function, we present an optimal investment theorem and simultaneously treat the corresponding dual problem.

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We provide the solution to a fusion of two fundamental problems in mathematical finance. The first problem is that of maximizing the expected utility of terminal wealth of an investor who holds a short position in a contingent claim, and the second is that of maximizing terminal wealth where the utility function allows the investor to have negative wealth. Under assumptions of reasonable asymptotic elasticity on the investor's utility function, we present an optimal investment theorem and simultaneously treat the corresponding dual problem.

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Available abstract

We provide the solution to a fusion of two fundamental problems in mathematical finance. The first problem is that of maximizing the expected utility of terminal wealth of an investor who holds a short position in a contingent claim, and the second is that of maximizing terminal wealth where the utility function allows the investor to have negative wealth. Under assumptions of reasonable asymptotic elasticity on the investor's utility function, we present an optimal investment theorem and simultaneously treat the corresponding dual problem.

Key concepts: Expected utility hypothesis, Terminal (telecommunication), Mathematics, Mathematical economics, Incomplete markets, Isoelastic utility, Dual (grammatical number), Transferable utility

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