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Barrier present value maximization for a diffusion model of insurance surplus

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  • Shangzhen Luo
  • Mingming Wang

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.

Suggested Citation

  • Shangzhen Luo & Mingming Wang, 2016. "Barrier present value maximization for a diffusion model of insurance surplus," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(10), pages 905-931, November.
    • Handle: RePEc:taf:sactxx:v:2016:y:2016:i:10:p:905-931
    DOI: 10.1080/03461238.2015.1031165
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