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

Weiwei Shen and Juliang Yin ()
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Weiwei Shen: Guangzhou University
Juliang Yin: Guangzhou University

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 4, 2913-2931

Abstract: Abstract 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.

Keywords: Optimal control; Stochastic economic factor; Lévy processes; PIDE; HARA utility; Viscosity solution; 49J20; 93E20; 91G80 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-022-09964-z

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