In this article, we investigate the MEMM (Minimal relative Entropy Martingale Measure) of Birth and Death processes and the MEMM of generalized Birth and Death processes. We see that the existence problem of the MEMM is reduced to the problem of solving the corresponding Hamilton-Jacobi-Bellman equation.

We discuss optimal portfolio selection with respect to utility functions of type −e−αx, α > 0 (exponential problem) and −|1 − αx p |p (p-th problem). We consider N risky assets and a risk-free bond. Risky assets are modeled by continuous semimartingales or exponential Lévy processes. These dynamic expected utility maximization problems are solved by transforming the model into a constrained sta...

In this paper, we consider structure preserving measure transforms for time-changed Lévy processes. Within this class of transforms preserving the time-changed Lévy structure, we derive equivalent martingale measures minimizing relative q-entropy. Structure preservation is found to be an inherent property of minimal q-entropy martingale measures under continuous time changes, whereas it imposes...

We give a unified characterization of q-optimal martingale measures for q ∈ [0,∞) in an incomplete market model, where the dynamics of asset prices are described by a continuous semimartingale. According to this characterization the variance-optimal, the minimal entropy and the minimal martingale measures appear as the special cases q = 2, q = 1 and q = 0 respectively. Under assumption that the...

The [GLP & MEMM] pricing model (= [Geometric Lévy Process & Minimal Entropy Martingale Measure] pricing model) has been introduced as a pricing model for the incomplete financial market. This model has many good properties and is applicable to very wide classes of underlying asset price processes including the geometric stable processes. We explain those good properties and see several examples...