随机利率与随机波动率模型下保险公司最优投资与再保险问题研究

项目名称： 随机利率与随机波动率模型下保险公司最优投资与再保险问题研究

项目编号： No.11301376

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 赵慧

作者单位： 天津大学

项目金额： 22万元

中文摘要： 本项目拟基于各类随机波动率模型和随机利率结构研究不同风险模型下的保险公司投资与再保险问题。首先以保险公司终端财富的期望效用最大、均值-方差最优为目标，针对常方差弹性(CEV)模型、Heston随机波动率模型、带跳的随机波动率模型建立相应的投资与再保险问题，采用随机控制理论求解跳扩散模型等时间齐次风险模型下的最优策略。然后考虑仿射随机利率模型（包含Cox-Ingersoll-Ross（CIR）模型和Vasicek模型）和Ho-Lee随机利率模型下的保险公司投资与再保险问题，以最大化终端财富的期望效用和最小化破产概率为目标，应用随机控制理论和鞅方法求解最优策略。最后，拟将风险模型推广到更加符合实际的非时间齐次风险过程，如周期风险模型和马氏调节风险模型，并扩展现有风险模型以更好地模拟实际，研究随机市场环境下基于非时间齐次风险模型的最优投资与再保险问题。

中文关键词： 随机波动率模型；随机利率模型；随机控制；Hamilton-Jacobi-Bellman(HJB)方程；投资再保险

英文摘要： This research considers the optimal investment and reinsurance problem for insurers with different risk processes under stochastic volatility and stochastic interest rate models. Firstly, we plan to study the optimization problem of maximizing the expected utilities of insurers' terminal wealth and optimizing the mean-variance problem for insurers with different time-homogeneous processes. Optimal strategies under the constant elasticity of variance (CEV) model, Heston model and stochastic volatility model with jump will be obtained by using techniques of stochastic control theory. Secondly, we will consider the optimal investment and reinsurance problem under the Ho-Lee interest rate model and interest rate model described by an affine dynamics which includes the Cox-Ingersoll-Ross (CIR) model and the Vasicek model as special cases. For objectives such as maximizing the expected utilities of insurers' terminal wealth and minimizing the ruin probability, we try to find optimal strategies via stochastic control approach and martingale method. Finally, the risk models will be extended into time-inhomogeneous risk processes such as periodic risk model and Markov-modulated risk model and more practical risk models will be proposed. We will study the optimal investment and reinsurance problem for insurers with time-i

英文关键词： Stochastic volatility model；Stochastic interest rate model；Stochastic control；Hamilton-Jacobi-Bellman(HJB) equation；investment and reinsurance