A Semimartingale Bellman Equation and the Variance-Optimal Martingale Measure

Abstract

Abstract We consider a financial market model, where the dynamics of asset prices is given by an R m -valued continuous semimartingale. Using the dynamic programming approach we obtain an explicit description of the variance optimal martingale measure in terms of the value process of a suitable problem of an optimal equivalent change of measure and show that this value process uniquely solves the corresponding semimartingale backward equation. This result is applied to prove the existence of a unique generalized solution of Bellman's equation for stochastic volatility models, which is used to determine the variance-optimal martingale measure.

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