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Optimal investment and reinsurance for an insurer under Markov-modulated financial market |
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| Affiliation: | 1. School of Mathematics and Computer Science, Anhui Normal University, Wuhu, Anhui, China;2. School of Finance, Nanjing University of Finance and Economics, Nanjing, Jiangsu, China;1. School of Statistics, East China Normal University, Shanghai 200241, PR China;2. School of Mathematical Science, Nanjing Normal University, Jiangsu 210023, PR China;1. School of Mathematics and Statistics, Zhaoqing University, Guangdong, 526061, PR China;2. Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada N2L 3C5;1. School of Sciences, Hebei University of Technology, Tianjin 300401, PR China;2. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA;1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, PR China;2. Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA;3. School of Finance, Guangdong University of Foreign Studies, Guangzhou 510006, China |
| Abstract: | This study examines optimal investment and reinsurance policies for an insurer with the classical surplus process. It assumes that the financial market is driven by a drifted Brownian motion with coefficients modulated by an external Markov process specified by the solution to a stochastic differential equation. The goal of the insurer is to maximize the expected terminal utility. This paper derives the Hamilton–Jacobi–Bellman (HJB) equation associated with the control problem using a dynamic programming method. When the insurer admits an exponential utility function, we prove that there exists a unique and smooth solution to the HJB equation. We derive the explicit optimal investment policy by solving the HJB equation. We can also find that the optimal reinsurance policy optimizes a deterministic function. We also obtain the upper bound for ruin probability in finite time for the insurer when the insurer adopts optimal policies. |
| Keywords: | Optimal investment Reinsurance Markov modulated risk model HJB equation Ruin probability |
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