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

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 di...

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Bibliographic Details
Published inMethodology and computing in applied probability Vol. 24; no. 4; pp. 2913 - 2931
Main Authors Shen, Weiwei, Yin, Juliang
Format Journal Article
LanguageEnglish
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
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-022-09964-z