关键词: Stochastic control, constant barrier, time of ruin, expected discounted dividend payment, moments, Laplace transform of the time of ruin

Abstract:

In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then get the optimal stochastic control and the optimal constant
barrier. Secondly, under the optimal constant dividend barrier strategy, we consider the moments of the discounted dividend payment and their explicit expressions are given. Finally, we discuss the Laplace transform of the time of ruin and its explicit expression is also given.

Key words: Stochastic control, constant barrier, time of ruin, expected discounted dividend payment, moments, Laplace transform of the time of ruin