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Optimal Investment and Risk Control for An Insurer in A Jump-diffusion Market with Regime-switching

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  • Weiwei Shen

    (Tongling University, School of Mathematics and Computer Science)

Abstract

This paper investigates optimal investment and risk control strategies for an insurer operating in a jump-diffusion market with regime-switching. The proposed model incorporates a risk-free asset, a risky asset governed by a Markov-modulated jump-diffusion stochastic differential equation (SDE), and a risk process negatively correlated with the risky asset, approximated by a diffusion process. The insurer manages wealth allocation and adjusts risk exposure via the number of insurance policies issued. Optimal strategies are derived within an expected utility maximization framework for logarithmic and power utility functions. For logarithmic utility, classical optimization under a strengthened budget constraint yields explicit solutions. Under power utility, the regime-switching Hamilton–Jacobi–Bellman (HJB) equation is solved to obtain closed-form strategies. Numerical simulations under a two-state Markov chain illustrate the optimal strategies for both utility functions.

Suggested Citation

  • Weiwei Shen, 2025. "Optimal Investment and Risk Control for An Insurer in A Jump-diffusion Market with Regime-switching," Methodology and Computing in Applied Probability, Springer, vol. 27(4), pages 1-29, December.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:4:d:10.1007_s11009-025-10228-9
    DOI: 10.1007/s11009-025-10228-9
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