Research On Asset-liability Management Issues Under The HESTON Model

In real life,there are limitations because of many scholars study the asset-liability management problem only rely on the assumption of constant volatility.Instead the volatility is a constant,it is random changing.On the other hand,according to the asset-liability management problem of the existing research results,we can see portfolio selection problem with liability process is more universal,and the application of Heston ’s stochastic volatility can describe the randomness of the stock price fluctuations.Therefore the asset-liability management problem under the Heston’s stochastic volatility environment that need to be further research.Based on it,this paper’s main work and obtain the results as follows:Firstly,we use stochastic optimal control theory to study a dynamic portfolio selection problem with liability process under the Heston’s stochastic volatility model.Stock price is assumed to be governed by the Heston model,the liability process is supposed to be driven by the drifted Brownian motion.The financial market consists of one risk-free asset and one risky asset.The explicit solutions to the optimal investment strategies under power utility and exponential utility is obtained by using stochastic dynamic programming principle and variable separation method.Finally,a numerical example is given to illustrate the effect of market parameters on the optimal investment strategy.Secondly,on the basis of the above model.Then,the preference degree of investors for risks can be described by HARA utility function,and the explicit solutions to the optimal investment strategies under HARA utility criterion is successfully obtained by using Legendre transformation method and variable separation technique.Finally,a numerical example is given to illustrate the effect of some market parameters on the optimal investment strategy.Thirdly,on the basis of the above model,we study mean-variance asset-liability management strategy under the Heston ’s stochastic volatility model.We apply stochastic dynamic programming principle and Lagrange dual theory and variable separation technique to achieve the explicit solutions of the efficient strategy under mean-variance criterion.Finally,a numerical example is given to illustrate the effect of some market parameters on the optimal investment strategy.