Characterisation of optimal dual measures via distortion (Q882491)

The paper analyses optimal measures in a two-factor Markovian market containing a stock \(S\) and a stochastic volatility \(Y\), driven by two correlated Brownian motions, \(W\) and \(\widetilde{W}\), respectively, with fixed correlation. The parameters of the stochastic differential equation for \(S\) are supposed to be progressively measurable with respect to the filtration generated by \(\widetilde{W}\). The author exploits an explicit solution known as a distortion power solution for a primal utility maximization problem, and seeks ramifications for the dual to the primal problem. The relations between the optimal martingale measure of the dual problem and the measure \(\widetilde{P}^M\) in the distortion solution, which is related to the minimal martingale measure (as some projection in the case of exponential utility) are studied. An alternative method to existing ones is proposed for characterising optimal measures and the new results are presented in the form of Esscher transform relations between the optimal measure and the minimal measure.