Abstract
We consider consumption-investment problems in a financial market with general random coefficients where the market price of risk process is unknown. The investor tries to maximize his expected utility under the worst-case parameter configuration. To solve robust consumption-investment problems, we make use of stochastic Bellman–Isaac equations. These equations can be explicitly solved for power, exponential and logarithmic utility. This enables us to characterize a robust optimal consumption-investment strategy and a worst-case market price of risk process in terms of the solution of a backward stochastic differential equation.
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