具有异常波动市场的消费与投资策略

讨论了异常波动市场中容许借贷的消费与投资策略问题,阐述了随机最优控制理论应用于现代金融理论研究中的一种方法.首先给出了金融市场中不确定性的随机模型,利用It^o公式,得到了与消费及投资策略有关的财富过程的随机微分方程,并建立了最优消费与投资问题的随机控制模型.根据随机最优控制理论,导出了目标函数满足的Hamilton-Jacobi-Bellman(HJB)方程.通过对HJB方程的讨论,得到了最优消费与投资策略的分段表示函数,并就Hara效用函数进行讨论,得到了具体的消费与投资策略.

Optimal consumption and investment policies in the marketwith abnormal fluctuating source

For the market with abnormal fluctuating source,the decision of consumption and investment is studied and a method that uses stochastic optimal control in financial theory is proposed.First of all,the stochastic model about uncertainty in financial market was introduced.By using Ito formula,the stochastic differential equation for fortune that was concerned with the decision of consumption and investment was given,the stochastic control model for consumption and investment was established.By using stochastic optimal control theory,the Hamilton_Jacobi_Bellman (HJB) equation for target function was gotten.By discussing the HJB equation,some pathwise function based optimal decision was acquired.Finally,the decision for Hara function was given.