This paper studies an optimal investment-reinsurance problem for an insurance company which is subject to a dynamic Value-at-Risk (VaR) constraint in a Markovian regime-switching environment. Our goal is to minimize its ruin probability and control its market risk simultaneously. We formulate the problem as an infinite horizontal stochastic control problem with the constrained strategies. The dynamic programming technique is applied to derive the coupled Hamilton-Jacobi-Bellman (HJB) equations and the Lagrange multiplier method is used to tackle the dynamic VaR constraint. Furthermore, we propose an efficient numerical method to solve those HJB equations. Finally, we employ a practical example from the Korean market to verify the numerical method and analyze the optimal strategies under different VaR constraints.

中文翻译：

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具有制度转换和风险价值约束的最优投资-再保险政策

本文研究了在马尔可夫体制转换环境下受动态风险价值（VaR）约束的保险公司的最优投资再保险问题。我们的目标是最大程度地降低其破产概率并同时控制其市场风险。我们将该问题表述为具有约束策略的无限水平随机控制问题。应用动态规划技术来推导耦合的Hamilton-Jacobi-Bellman（HJB）方程，并使用拉格朗日乘数法来解决动态VaR约束。此外，我们提出了一种有效的数值方法来求解这些HJB方程。最后，我们以韩国市场为例，验证了数值方法并分析了在不同VaR约束下的最优策略。