Optimal Investment-Consumption Choice with Portfolio Constraint in Ambiguity Market

In this paper, we consider an optimal investment-consumption choice problem with portfolio constraint, where the expected return rate and volatility are uncertain. We formulate it into an optimal stochastic control problem, and then transform it into a saddle point problem of a function with constraint via some existing results. Finally, we provide the explicit form of the optimal investment-consumption strategies and the worst-case parameters, and give some financial explanation about some results.