Vasicek利率与Heston模型下的最优投资和再保险  

Optimal Investment and Reinsurance Under Vasicek Interest Rate and Heston Model

作　　者：聂高琴[1] 常浩[2] NIE Gaoqin;CHANG Hao(School of statistics,Capital University of Economics and Business,Beijing 100070,China;School of Science,Tianjin Polytechnic University,Tianjin 300387,China)

机构地区：[1]首都经济贸易大学统计学院,北京100070 [2]天津工业大学理学院,天津300387

出　　处：《应用数学》2020年第2期525-533,共9页Mathematica Applicata

基　　金：北京市教委科研计划项目(SM201810038008);北京市自然科学基金项目(1182007);首都经济贸易大学校级科研项目(2017XJQ005)。

摘　　要：本文主要研究Vasicek随机利率模型下保险公司的最优投资与再保险问题.假设保险公司的盈余过程由带漂移的布朗运动来描述,保险公司通过购买比例再保险来转移索赔风险;同时,将财富投资于由一种无风险资产与一种风险资产组成的金融市场,其中,利率期限结构服从Vasicek利率模型,且风险资产价格过程满足Heston随机波动率模型.利用动态规划原理及变量替换的方法,得到了指数效用下最优投资与再保险策略的显示表达式,并给出数值例子分析了主要模型参数对最优策略的影响.This paper mainly studies the optimal investment and reinsurance strategy of the insurance company under Vasicek stochastic interest rate model.In this paper,the surplus process of insurance company is described by the Brownian motion with drift.Insurance company transfer claim risk by purchasing proportional reinsurance and investing wealth in the financial market consisting of a risk-free asset and a risky asset.The term structure of interest rate is assumed to follow Vasicek interest rate,and the price process of the risky asset is assumed to follow Heston stochastic volatility model.By using the dynamic programming principle and the variable change technique,the explicit expression of the optimal investment and reinsurance strategy for the exponential utility is obtained,and a numerical example is given to analyze the impact of main model parameters on the optimal strategy.

关 键 词：VASICEK利率模型 Heston随机波动率模型 比例再保险 指数效用 

分 类 号：F840[经济管理—保险]