Optimization of the Cramer Lundberg model based value function of reinsurance with random claims and new premium arrival

Abstract

In general, an insurance company who experiences two opposing cash flows incoming cash premiums and outgoing claims that is also known as classical risk process that satisfies Cramér–Lundberg model. However the arrival of the new premium holders and there cash flow over a period of time was not considered in most works. In this model, we considered the arrival of new premiums with expectation of surplus process until ruin time with dynamic reinsurance strategy. For attaining this condition, we formulated a Value function which is bounded and satisfied by the Hamilton Jacobi Bellman (HJB) partial differential equation. We apply the policy iteration method to find the maximum the surplus level and corresponding dynamic reinsurance strategy under excess of loss, quota share and stop loss reinsurance problems.