  In the classical static optimal reinsurance problem, the cost of capital for
the insurer's risk exposure determined by a monetary risk measure is minimized
over the class of reinsurance treaties represented by increasing Lipschitz
retained loss functions. In this paper, we consider a dynamic extension of this
reinsurance problem in discrete time which can be viewed as a risk-sensitive
Markov Decision Process. The model allows for both insurance claims and premium
income to be stochastic and operates with general risk measures and premium
principles. We derive the Bellman equation and show the existence of a
Markovian optimal reinsurance policy. Under an infinite planning horizon, the
model is shown to be contractive and the optimal reinsurance policy to be
stationary. The results are illustrated with examples where the optimal policy
can be determined explicitly.
