We study the existence and uniqueness of martingale measures in the exponential Levy models of the form $S_t=e^{X_t}$, $S_t=e^{X_{\tau_t}}$, where X is a Levy process and $\tau$ is an independent increasing process.
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.
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.