广义奇异控制下最优风险控制和红利优化策略的数值解
Numerical Solutions of Optimal Risk Control and Dividend Optimization Policies under A Generalized Singular Control Formulation
摘要：
本文发展了求解最优红利支付和再保险策略的数值方法。引入了一种广义奇异控制的盈余和折扣支付函数，其中盈余模型的状态切换过程受到常规和奇异控制。为了逼近价值函数和最优控制，利用马尔可夫链逼近技术构造了一个具有两个分量的离散时间受控马尔可夫链。给出了逼近序列收敛于盈余过程和值函数的证明。比例和超额损失再保险的例子来说明数值方法的适用性。
英文摘要：
This paper develops numerical methods for finding optimal dividend pay-out and reinsurance policies. A generalized singular control formulation of surplus and discounted payoff function are introduced, where the surplus is modeled by a regime-switching process subject to both regular and singular controls. To approximate the value function and optimal controls, Markov chain approximation techniques are used to construct a discrete-time controlled Markov chain with two components. The proofs of the convergence of the approximation sequence to the surplus process and the value function are given. Examples of proportional and excess-of-loss reinsurance are presented to illustrate the applicability of the numerical methods.
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