Minimal q-entropy martingale measures for exponential time-changed Lévy processes

Abstract

We consider structure preserving measure transforms for time-changed Levy processes. Within this class of transforms preserving the time-changed Levy structure, we derive equivalent martingale measures minimizing relative q-entropy. They combine the corresponding transform for the Levy process with an Esscher transform on the time change. Structure preservation is found to be an inherent property of minimal q-entropy martingale measures under continuous time changes, whereas it imposes an additional restriction for discontinuous time changes.