Stochastic orders in dynamic reinsurance markets

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 minimal martingale measure and the minimal entropy martingale measure are determined, and some comparison results for prices under different martingale measures are provided. This leads to a simple stochastic ordering result for the optimal martingale measures. Moreover, these optimal martingale measures are compared with other martingale measures that have been suggested in the literature on dynamic reinsurance markets.

Keywords: Compound Poisson process, change of measure, minimal martingale measure, minimal entropy martingale measure, convex order, stop-loss contract.