CEV模型下基于双曲绝对风险厌恶效用的最优投资策略

研究双曲绝对风险厌恶(HARA)型投资者在常弹性方差(CEV)模型下面临完全可对冲随机资金流时的最优动态资产配置问题.随机资金流可以视作一个外生负债,假定其服从带漂移的布朗运动.根据随机控制理论建立该问题的哈密顿-雅克比-贝尔曼(HJB)方程,通过猜测值函数的代数形式,将其化简为两个抛物型偏微分方程并分别求得显式解,从而得到最优投资策略.结果表明该非自融资组合的最优动态配置问题等价于初始财富为所有未来随机净资金流在风险中性测度下累积期望现值与初始稟赋之和的自融资组合的最优动态配置问题.投资策略由短视投资策略,动态对冲策略,静态对冲策略三部分组成.当对模型中参数取特殊值时,策略简化为已有文献的相应结果.最后分析了参数变化对于由随机资金流引起的额外投资需求的影响.

Optimal investment policy for hyperbolic absolute risk averse utility function under the CEV model

This paper investigates the optimal portfolio choice problem for an investor with hyperbolic absolute risk averse utility over terminal wealth facing perfectly hedgeable stochastic cash flow under the constant elasticity of variance (CEV) model. The cash flow can be interpreted as an exogenous liability and is assumed to follow a Brownian motion with drift. Using techniques of stochastic optimal control, we first derive the corresponding Hamilton-Jacobi-Bellman (HJB) equation, and then reduce it into two parabolic partial differential equations (PDES) by directly conjecturing the functional form of the corresponding value function. Finally, by finding explicit solutions of the pdes we obtain the optimal investment policy. We show that the optimal non-self-financing portfolio choice problem is equivalent to a self-financing portfolio choice problem with its initial wealth equal to the sum of the endowment of the non-self-financing one and the cumulative discounted expectation of the stochastic cash flow with respect to risk neutral probability measure. Besides the familiar myopic and dynamic hedging demand, there is an additional components, the static hedging demand to hedge the risk of stochastic cash flow in the optimal strategy. The optimal policies reduce to previous results as the parameters in the model take special values. Finally, a numerical example is also provided to demonstrate the effect of parameters on the additional investment demands.