A semimartingale Bellman equation and the variance-optimal martingale measure (Q2709768)

This paper studies the problem of describing the variance-optimal martingale measure \(Q^*\) in a setting where the underlying price process is a multidimensional continuous semimartingale and the filtration is continuous. The main result shows that the value process for the problem of finding \(Q^*\) is the unique solution of a semimartingale backward equation. This is used to give equivalent characterizations of \(Q^*\). For the case of an Itô process model, the above equation becomes a backward stochastic differential equation; in the Markovian case, the corresponding Bellman equation generalizes results by \textit{J. P. Laurent} and \textit{H. Pham} [Finance Stoch. 3, 83-110 (1999; Zbl 0924.90021].