Research On Investment-consumption Issues Under Stochastic Interest Rates And Stochastic Volatility

Investment-consumption problem is the most important content of fanan-cial engineering,and is a hot area of research of continuous time protfolio selec-tion problem.It answers the question,how distribute people' s wealth to a vari-aty of assets to maximize the expected yield when they spent their money.Most of existing literature focused their attention on investment-consumption problem with constant interest rate or constant volatility.However,it is inconsistent to the real environment.Affected by many uncertainty factors(such as monetary poli-cy,inflation,financial policy,political events and psychological factor),interest rate and volatility are often not constant.In this case,investors had made their efforts to investment-consumption problem in stochastic environment and achieved fruitful results.While most of this results dedicated themsevels to investment-consumption problem in single risk environment,and they have not think the influence of differ-ent utility fuctions.HARA utility function contains power utility function,expo-nential utility function and logrithmic utility function as special cases,and it is the most general utility function.Due to it' s complicated expression,the achievements on this aspect is seldom before.According these defects,we updated the existing research on investment-consumption problem,the main working as follows:First,we studied invetment problem in CIR model.In this section,we assume that,financial market is consist of a free-risk asset,a large number of risk asset and a zero coupon bond.We got the explicit solution of optimal investment strategy in HARA utility.Second,we studied investment-consumption problem in stochastic affine rate and stochastic volatility.We assume that stock price is affected by stock mar-ket fluctuation and rate fluctuation,and volatility obey Heston model.We pur-sue the expected utility of intermediate consumption and terminal wealth as our objective function,and obtained the explicit solution of optimal investment-consumption strategy by using dynamic programming principle and variable sub-stitution method.At last,we analyzed the impact of interest rate and volatility on optimal investment-consumption strategies by numerical examples.Third,we extended investment-consumption problem to CEV model,and as-sume that investors'risk aversion on risk satisfied HARA utility function.We got the explicit solution of optimal investment-consumption strategy by using dynam-ic programming principle and Ledgendre transform method,and we analyzed the impact of market parameters on optimal investment-consumption strategy by nu-merical examples.