Abstract

In this paper, we study how to estimate the optimal dividend strategy in a discrete-time risk model with delayed claims. The insurance company pays dividends to shareholders, and each dividend is taxable. The company controls the dividend payments to maximize the expectation of accumulated discounted dividends after tax prior to ruin. This paper aims to develop a method to estimate the optimal dividend strategy by using historical data directly. For the purpose we construct a nonlinear stochastic operator on the space $l^{\infty },$ which is proved to have contraction property. Fortunately the stochastic fixed point of the operator converges to a real sequence in probability, from which a consistent estimator of the optimal strategy follows. This is an important advantage of the stochastic operator method because the consistency property is difficult to be obtained by traditional methods with estimated distributions for claims. Finally, the method is applied in an example. The estimation results by using simulation data show that the optimal dividend strategy is a conditional threshold strategy, and the optimal dividend threshold tends to be stable with the sample size increasing.

摘要

在本文中，我们研究了如何在具有延迟索赔的离散时间风险模型中估计最优股息策略。保险公司向股东支付股息，每笔股息都应纳税。公司控制股息支付，以最大限度地提高破产前税后累计贴现股息的预期。本文旨在开发一种直接利用历史数据来估计最优分红策略的方法。为此，我们在空间上构造了一个非线性随机算子$l^{\infty },$证明具有收缩性。幸运的是，算子的随机不动点在概率上收敛到一个真实的序列，从中可以得到最优策略的一致估计。这是随机算子方法的一个重要优点，因为一致性属性很难通过具有估计索赔分布的传统方法获得。最后将该方法应用到一个例子中。仿真数据估计结果表明，最优分红策略是一种条件阈值策略，随着样本量的增加，最优分红阈值趋于稳定。