Optimal decisions for an insurance contract with experience rating

In this paper the authors consider the insurance of assets with experience rating in the framework of a discrete-time dynamic decision model. The goal of the risk-averse agent (insurance buyer) is to maximize the expected utility of wealth at the finite planning horizon. First, it has to be decided whether a contract should be bought or not. The contract gives the possibility to choose in each period between three alternatives: to buy insurance and to file a claim, to buy insurance and not to file a claim, to suspend insurance. For this case structural properties of the optimal strategy are obtained by means of dynamic programming. Especially, the authors present a condition for the experience rating scheme such that the decision to suspend insurance is irreversible during the planning period (stopping rule). In the final section they present some numerical experiences. Among others it will be shown that the optimal decision functions generally are not monotone with respect to the agent’s claim history.