A class of stochastic volatility models and the <italic>q</italic>-optimal martingale measure

This paper proposes an approach under which the <italic>q</italic>-optimal martingale measure, for the case where continuous processes describe the evolution of the asset price and its stochastic volatility, exists for all finite time horizons. More precisely, it is assumed that while the ‘mean--variance trade-off process’ is uniformly bounded, the volatility and asset are imperfectly correlated. As a result, under some regularity conditions for the parameters of the corresponding Cauchy problem, one obtains that the <italic>q</italic>th moment of the corresponding Radon--Nikodym derivative does not explode in finite time.