We consider a dynamic reinsurance market, where the traded risk process is driven by a jump-diffusion and where claim amounts are unbounded. These markets are known to be incomplete, and there are typically infinitely many martingale measures. In this case, no-arbitrage pricing theory can typically only provide wide bounds on prices of reinsurance claims. Optimal martingale measures such as the...

We give a sufficient condition to identify the q-optimal signed and the q-optimal absolutely continuous martingale measures in exponential Lévy models. As a consequence we find that, in the onedimensional case, the q-optimal equivalent martingale measures may exist only, if the tails for upward jumps are extraordinarily light. Moreover, we derive convergence of the q-optimal signed, resp. absol...

We develop a technique based on Malliavin-Bismut calculus ideas, for asymptotic expansion of dual control problems arising in connection with exponential indifference valuation of claims, and with minimisation of relative entropy, in incomplete markets. The problems involve optimisation of a functional of Brownian paths on Wiener space, with the paths perturbed by a drift involving the control....

The Esscher transform is one of the very useful methods to obtain the reasonable equivalent martingale measures, and it is defined with relation to the corresponding risk process. In this article we consider two kinds of risk processes (compound return process and simple return process). Then we obtain two kinds of Esscher transformed martingale measures. The first one is the one which was intr...

In this paper we review the relative entropy meathods for the option pricing theory in the incomplete markets. First we summarize the known results with respect to the existence of minimal relative entropy martingale measure (MEMM), and then we give several examples of the pricing models related to the MEMM (for example, the [Geometric Lévy & MEMM] pricing model). After that we explain the math...