Barrier present value maximization for a diffusion model of insurance surplus

Shangzhen Luo and Mingming Wang

Scandinavian Actuarial Journal, 2016, vol. 2016, issue 10, 905-931

Abstract: 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.

Date: 2016
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DOI: 10.1080/03461238.2015.1031165

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