We introduce a general framework for stochastic volatility models, with the risky asset dynamics given by: where (ω,η)∈(ΩH,F^Ω⊗F^H,P^Ω⊗P^H).

In particular, we allow for random discontinuities in the volatility σ and the drift μ. First we characterize the set of equivalent martingale measures, then compute the mean-variance optimal measure , using some results of Schweizer on the existence of an adjustment process β.

We show examples where the risk premium λ=(μ-r)/σ follows a discontinuous process, and make explicit calculations for .