Optimal consumption-investment problems in incomplete markets with random coefficients

In this work we present the explicit solution of an optimal investment problem in an incomplete financial market, for HARA and logarithmic utility functions. The market follows a generalization of the Black and Scholes diffusion model, which consists of a bank account, a risky asset, and an economic external factor. The coefficients of the underlying diffusion processes are random and depend on the economic external factor. This market includes more realistic financial scenarios where the martingale methodology and stochastic control techniques, established in Castafieda-Leyva and Hernandez-Hernandez [2], are applied.