CEV模型下家庭最优投资决策问题  

Family Optimal Investment Decision-making Problem Under CEV Model

作　　者：周双龙 王爱银[1] ZHOU Shuang-long;WANG Ai-yin(Institute of Statistics and Data Science,Xinjiang University of Finance&Economics,Urumqi 830012,China)

机构地区：[1]新疆财经大学统计与数据科学学院,新疆乌鲁木齐830012

出　　处：《数学的实践与认识》2021年第5期45-55,共11页Mathematics in Practice and Theory

基　　金：国家社会科学基金一般项目“基于CEV模型的中国居民金融资产投资-储蓄-经济增长策略的研究”(18BJL072);硕士研究生科研创新项目“基于跳-扩散下资产投资-储蓄-增长策略研究”(XJUFE2020K010)。

摘　　要：考虑固定收入下具有随机支出风险的家庭最优投资组合决策问题.在假设投资者拥有工资收入的同时将财富投资到一种风险资产和一种无风险资产,其中风险资产的价格服从CEV模型,无风险利率采用Vasicek随机利率模型.当支出过程是随机的且服从跳-扩散风险模型时,运用动态规划的思想建立了使家庭终端财富效用最大化的HJB方程,采用Legendre-对偶变换进行求解,得到最优策略的显示解,并通过敏感性分析进行验证表明,家庭投资需求是弹性方差系数的减函数,解释了家庭流动性财富的增加对最优投资比例呈现边际效用递减趋势.In this paper,we consider the optimal portfolio decision of families with random expenditure risk under fixed income.On the assumption that investors have wage income,they invest wealth into a risky asset and a risk-free asset,in which the price of risky asset follows CEV model and the risk-free interest rate adopts Vasicek stochastic interest rate model.When the expenditure process is random and follows the jump-diffusion risk model,the HJB equation is established by using the idea of dynamic programming,and the Legendre-dual transformation is used to solve the equation,and the explicit solution of the optimal strategy is obtained.The sensitivity analysis shows that the household investment demand is a decreasing function of the elastic variance coefficient,which explains that the increase of household liquidity wealth shows a decreasing trend of marginal utility to the optimal investment ratio.

关 键 词：CEV模型 跳-扩散 随机支出 LEGENDRE变换 最优策略 

分 类 号：F224[经济管理—国民经济] F832.5