On Martingale Measures for Stochastic Processes with Independent Increments

Abstract

We consider a special semimartingale X with independent increments and prove the existence and equivalence of a local martingale measure {\bf P}$^H$ for~X, which minimizes the Hellinger process under the assumption that there exists an equivalent local martingale measure for~X. This is done under the restriction of quasi-left-continuity and boundedness of jumps of~X. Furthermore, we investigate the relation between the well-known minimal martingale measure {\bf P}$^{\min}$ and {\bf P}$^H$. It is shown that in a sense {\bf P}$^{\min}$ is an approximation of~{\bf P}$^H$.