Optimal Consumption-Investment Problems in Incomplete Markets with Stochastic Coefficients

The goal of this paper is to solve an optimal consumption-investment problem in the context of an incomplete financial market. The model is a generalization of the Black and Scholes diffusion model, where the coefficients of the diffusion modelling the stockʹs price depend on some stochastic economic factors. Based on the martingale approach, a basic methodology to get the optimal solution is presented. Combining this procedure with stochastic control techniques, explicit solutions for HARA and logarithmic utility functions are obtained.