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Vasicek利率与Heston模型下的最优投资和再保险
引用本文:聂高琴,常 浩.Vasicek利率与Heston模型下的最优投资和再保险[J].应用数学,2020,33(2):525-533.
作者姓名:聂高琴  常 浩
作者单位: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
基金项目: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.

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
收稿时间:2019/5/23 0:00:00

Optimal Investment and Reinsurance Under Vasicek Interest Rate and Heston Model
NIE Gaoqin,CHANG Hao.Optimal Investment and Reinsurance Under Vasicek Interest Rate and Heston Model[J].Mathematica Applicata,2020,33(2):525-533.
Authors:NIE Gaoqin  CHANG Hao
Institution:(School of statistics,Capital University of Economics and Business,Beijing 100070,China;School of Science,Tianjin Polytechnic University,Tianjin 300387,China)
Abstract: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.
Keywords:Vasicek interest rate model  Heston stochastic volatility model  Proportional reinsurance  Exponential utility
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