Barrier present value maximization for a diffusion model of insurance surplus |
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Authors: | Shangzhen Luo Mingming Wang |
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Institution: | 1. Department of Mathematics, University of Northern Iowa, Cedar Falls, IA, USA.;2. School of Insurance, University of International Business &3. Economics, Beijing, China. |
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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. |
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Keywords: | barrier present value reinsurance investment HJB equation diffusion approximation |
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