2014•SIAM Journal on Control and OptimizationRequires access

Forward Backward Semimartingale Systems for Utility Maximization

Marina Santacroce, Barbara Trivellato

Abstract

We consider the problem of maximizing the expected utility of terminal wealth with a terminal random liability when the underlying asset price process is a continuous semimartingale. The optimal strategy is characterized in terms of a forward backward semimartingale system of equations. The results cover the cases of exponential, logarithmic, and power utilities, which we analyze as illustrative examples.

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Key concepts: Semimartingale, Exponential utility, Utility maximization, Mathematics, Utility maximization problem, Logarithm, Cover (algebra), Terminal (telecommunication)