论文标题
根据指数远期偏好的最佳投资和再保险
Optimal investment and reinsurance under exponential forward preferences
论文作者
论文摘要
我们研究了一家保险公司的最佳投资和比例再保险问题，其投资偏好是通过在随机因素模型中的指数类型的向前动态实用程序来描述的，从而允许金融和保险市场之间的依赖性。具体而言，我们假设资产价格过程动态和索赔到达强度都受到共同随机过程的影响，并且我们通过非零的相关参数来解释可能的环境传染效应，从而驱动资产价格过程的基础布朗尼运动与随机因子动态。通过随机控制技术，我们构建了一个前向动态指数实用程序，并且表征了最佳投资和再保险策略。此外，我们详细研究了零挥发性案例，并提供了比较分析，并在向后效用的偏好下以类似的环境进行了经典结果。我们还讨论有条件确定性的扩展。最后，我们执行数值分析以突出最佳策略的某些特征。
We study the optimal investment and proportional reinsurance problem of an insurance company, whose investment preferences are described via a forward dynamic utility of exponential type in a stochastic factor model allowing for a possible dependence between the financial and insurance markets. Specifically, we assume that the asset price process dynamics and the claim arrival intensity are both affected by a common stochastic process and we account for a possible environmental contagion effect through the non-zero correlation parameter between the underlying Brownian motions driving the asset price process and the stochastic factor dynamics. By stochastic control techniques, we construct a forward dynamic exponential utility, and we characterize the optimal investment and reinsurance strategy. Moreover, we investigate in detail the zero-volatility case and provide a comparison analysis with classical results in an analogous setting under backward utility preferences. We also discuss an extension of the conditional certainty equivalent. Finally, we perform a numerical analysis to highlight some features of the optimal strategy.
