The variance-optimal martingale measure for continuous processes

Abstract

We prove that for continuous stochastic processes S based on (Ω,F, P) for which there is an equivalent martingale measure Q⁰ with square-integrable density dQ⁰/dP, we have that the so-called `variance-optimal' martingale measure Q^opt for which the density dQ^opt/dP has minimal L²(P)-norm is automatically equivalent to P. The result is then applied to an approximation problem arising in mathematical finance.