Barrier Present Value Maximization For A Diffusion Model Of Insurance Surplus
barrier present value, diffusion approximation, HJB equation, investment, reinsurance
Scandinavian Actuarial Journal
In this paper, we study a barrier present value (BPV) maximization problem for an insurance entity whose surplus process follows an arithmetic Brownian motion. The BPV is defined as the expected discounted value of a payment made at the time when the surplus process reaches a high barrier level. The insurance entity buys proportional reinsurance and invests in a Black–Scholes market to maximize the BPV. We show that the maximal BPV function is a classical solution to the corresponding Hamilton–Jacobi–Bellman equation and is three times continuously differentiable using a novel operator. Its associated optimal reinsurance-investment control policy is determined by verification techniques.
Department of Mathematics
Original Publication Date
DOI of published version
UNI ScholarWorks, Rod Library, University of Northern Iowa
Luo, Shangzhen and Wang, Mingming, "Barrier Present Value Maximization For A Diffusion Model Of Insurance Surplus" (2016). Faculty Publications. 1001.