The minimal entropy martingale measures for geometric Lévy processes
The authors establish the existence of the minimal entropy martingale measures (MEMMs) for the geometric Lévy processes \(\tilde{S}_t\) and show that the MEMM can be defined by means of the Esscher transformation of the return process for \(\tilde{S}_t\) which gives an explicit representation of the MEMM. A criterion is given for judging when conditions of the main theorems are fulfilled. For instance, compound Poisson processes, stable processes and variance gamma processes are good enough. It is also proved that MEMM price is the limit of the utility indifference price as the risk aversion parameter tends to 0.
scientific article; zbMATH DE number 2059115