管理工程学报2017，Vol.31Issue(2)：177-184,8.DOI:10.13587/j.cnki.jieem.2017.02.021
模型不确定下带通胀的最优消费和投资组合问题研究
Optimal consumption and portfolio under inflation and model uncertainty
摘要
Abstract
An investor is often faced with two types of uncertainties.One type is probability uncertainty or risk when variables related to environment have a known probability distribution.The other type is Knightian uncertainty or model uncertainty when information on the concerned phenomenon is not much available.When an investor makes a decision through a model,he/she is often concerned with the misspecification of a model and seeks robust decision rules.For an investor participating in a financial market,he/she is confronted with an optimal consumption and portfolio decision under a continuous time framework,which stems fiom Merton's initiating work in 1969 and 1971.Since then,many researchers further investigate this problem under different market hypotheses and obtain many significant results.Recently,the inflation factor has been included in the problem of the optimal consumption and portfolio,where an investor believes completely in the selected model.However,since the availability of market information is often ineffective,the suggested model could be misspecified.Thus,it is necessary to consider model uncertainty in modelling a financial market.Especially,it is necessary that both inflation and model uncertainty are incorporated in the model of an investor's optimal consumption and portfolio decisions.This paper studies the optimal consumption and portfolio in the case of inflation with the recursive preference of investors who seek robust decision rules.An investor partieipates in a financial market with a riskless asset (bond) and several risky assets (stocks).The investor's objective is to maximize the expected utility of consumption discounted by the inflation while he/she is considering the impact of the model misspeeification and inflation on the consumption and portfolio.Through the method of stochastic control,the corresponding HJB equation of an investor's value function is derived.For a special utility,the explicit solution to the problem of the optimal consumption and portfolio is obtained.Using a numerical simulation,we find that the concern about model uncertainty leads to a substantial reduction of myopic demand,causing the decline of the optimal equity allocation.However,when stock uncertainty and inflation uncertainty in the case of the low inflation volatility are considered a positive correlation relative to the non-inflationary situation,the inflation hedge demand increases the optimal equity allocation.When stock uncertainty and inflation uncertainty in the case of the high inflation volatility are considered,a negative correlation relative to the non-inflationary situation,the inflation hedge demand exacerbates the decline of the optimal equity allocation.Moreover,economic interpretations of our results are as follows.First,the ratio of wealth invested in risky stocks is affected by inflation fluctuation.In the case of low inflation,as real interest rates on deposits are negative interest rates,investors are more willing to increase the ratio of wealth invested in stocks in order to hedge currency devaluation losses.On the other hand,in the case of the high inflation,investors are less willing to put money in a bank and invest in stocks,but buy precious metals (gold,silver) with the hedging function.Second,as investors worry about the accuracy of the model,they usually consider the effect of the model misspecification on the portfolio.Thus,they will lower the ratio of wealth invested in risky assets accordingly.In summary,this paper characterizes the investor's decision with both probability and model uncertainty which are reflected in the problem of investor's optimal consumption and portfolio decisions.By the modem stochastic control theory,we have obtained some results which have both theoretic values and actual economic significance.关键词
模型不确定/通胀/投资组合/递归偏好/HJB方程Key words
Model uncertainty/Inflation/Portfolio/Recursive preferences/HJB equation分类
数理科学引用本文复制引用
费为银,费晨,夏登峰,杨武..模型不确定下带通胀的最优消费和投资组合问题研究[J].管理工程学报,2017,31(2):177-184,8.基金项目
国家自然科学基金资助项目(71171003,71271003) （71171003,71271003）
教育部人文社会科学规划基金资助项目(12YJA790041) （12YJA790041）
安徽省自然科学基金资助项目(090416225,1208085MG116) （090416225,1208085MG116）
