General Closed-Form Solutions To The Dynamic Optimization Problem In Incomplete Markets

In this paper, the authors provide general closed-form solutions to the incomplete-market random-coefficient dynamic optimization problem without the restrictive assumption of exponential or HARA utility function. Moreover, they explicitly express the optimal portfolio as a function of the optimal consumption and show the impact of optimal consumption on the optimal portfolio. Dynamic optimization has been used extensively in the economic and financial literature. Examples include incomplete markets, stochastic volatility and random coefficients models. The contemporary literature usually adopts random coefficient models (the parameters of the model are dependent on a random external economic factor) or non-tradable assets models.