模糊市场中含有投资约束的最优投资消费问题

Optimal Investment-Consumption Choice with Portfolio Constraint in Ambiguity Market

假设金融市场中的投资具有约束,期望回报率和波动率均具有不确定性.为了求出该市场中最优投资消费策略的表达式,首先建立鲁棒效用下的最优投资消费模型;然后将该模型转化为一个有约束条件的多元函数的鞍点问题,其中的鞍点对应着模型中的最优投资消费策略和最坏情形下的市场参数;最后给出最优投资消费策略和最坏情形下市场参数的显示表达式,并给出相应的金融解释.

The problem of optimal investment-consumption choice is studied,supposing that the investment is under constraint and the expected return rate and the volatility are uncertain. In order to obtain the formula of optimal investment-consumption strategies,a robust utility-oriented model of optimal investment-consumption is set up,and then it is transformed into a saddle point problem of a constrained multivariate function,with the saddle point corresponding to the optimal investment-consumption strategies and the worst-case parameters. Finally,the explicit formula of the optimal investment-consumption strategies and the worst-case parameters are provided,and a financial explanation about the results are given.