Optimal reinsurance strategy under fixed cost and delay
An optimal reinsurance strategy is considered where the insurance company (1) monitors the dynamics of its surplus process, (2) optimally chooses a time to begin negotiating with a reinsurer to buy quota-share, or proportional, reinsurance, which introduces an implementation delay (denoted by \(\Delta \geq 0\)), (3) chooses the optimal proportion at the beginning of the negotiation period, and (4) pays a fixed transaction cost when the contract is signed (\(\Delta \) units of time after negotiation begins). This setup leads to a combined problem of optimal stopping and stochastic control. A solution is obtained for the value function and the corresponding optimal strategy, while demonstrating the solution procedure in detail. It turns out that the optimal continuation region is a union of two intervals, a rather rare occurrence in optimal stopping. Numerical examples are given to illustrate the results and relevant economic insights from this model are discussed.
scientific article; zbMATH DE number 5539237
scientific article