The minimal entropy martingale measures for exponential additive processes
The author considers a real-valued additive process, that is, a stochastic process with independent increments (not obligatory with stationary increments) and supposes that this additive process is quasi-left continuous semimartingale. Exponential moments of such processes and connected stochastic integrals are calculated. The exponential additive process is considered as the price process of a risky asset and, under comparatively mild conditions on the semimartingale characteristics, the existence of minimal martingale measure is established. As an application, exponential utility maximization problem in the market model based on the exponential additive process is studied and the optimal strategy is deduced. Several examples are considered, such as time-dependent versions of double Poisson model, Merton model and Kou model.
scientific article; zbMATH DE number 5604985
scientific article