带有随机因子的最优投资和消费问题(英文)

Optimal Investment and Consumption Model with Stochastic Factor

研究了一类证券市场中随机最优投资组合和消费模型,模型允许中间消费和贴现因子,投资者可以随机的改变交易策略。债券的价格服从确定性的常微分方程而股票的价格服从一个扩散过程,并且受随机因子的影响。当投资者的投资行为满足CRRA型效用函数,运用动态规划方法和幂变换的方法,通过求解相应的Hamilton-Jacobi-Bellman(HJB)方程,将值函数表示为相应的伪线性偏微分方程的解,并得到了最优投资组合及消费选择的显示解,并给出了最优投资组合策略。

This paper deals with a class of stochastic optimization and consumption models in markets with stochastically changing investment opportunities,which is to allow for intermediate consumption and has the discount factor.The price of the bond is deterministic as opposed to the stock price which is modelled as a diffusion process whose coefficients evolved according to correlated diffusion factors.The individual preferences are of CRRA type.Under certain assumption on the individual preferences,we are able to produce reduced form solutions.Employing a power transformation,we express the value function in terms of the solution of a quasilinear partial differential equation,with the power exponent depending only on the coefficients of correlation and risk aversion.