Optimal Investment and Risk Control Strategies for an Insurer Subject to a Stochastic Economic Factor in a Lévy Market

• Published in: Methodology and computing in applied probability Vol. 24; no. 4; pp. 2913 - 2931
• Main Authors: Shen, Weiwei, Yin, Juliang
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2022; Springer Nature B.V
• Subjects: Business and Management; Capital gains; Default; Differential equations; Dynamic programming; Economic factors; Economics; Electrical Engineering; Expected utility; Life Sciences; Logarithms; Markov analysis; Mathematics and Statistics; Numerical analysis; Optimization; Portfolio investments; Risk management; Securities markets; Statistics; Strategy; Utility functions; Viscosity; Stochastic economic factor; 93E20; 49J20; Optimal control; Viscosity solution; Lévy processes; HARA utility; 91G80; PIDE
• DOI: 10.1007/s11009-022-09964-z
• ISSN: 1387-5841

Optimal investment and risk control problem for an insurer subject to a stochastic economic factor in a Lévy market is considered in this paper. In our mathematical model, a riskless bond and a risky asset are assumed to rely on a stochastic economic factor which is described by a Lévy stochastic differential equation (SDE). The risk process is described by a new “jump-diffusion” SDE depending on the stochastic economic factor and is negatively correlated with capital gains in the financial market. Using expected utility maximization, we characterize the optimal strategies of investment and risk control under the logarithmic utility function and the power utility function, respectively. With the logarithmic utility assumption, we use the classical optimization method to obtain the optimal strategy. However, for the power utility function, we apply dynamic programming principle to derive the Hamilton–Jacobi–Bellman (HJB) equation, and analyze its solution in order to obtain the optimal strategy. We also show the verification theorem. Finally, to study the impact of the market parameters on the optimal strategies, we conduct a numerical analysis.