An investment and consumption problem for quadratic utility function in an incomplete market

This paper is concerned with an investment and consumption problem in an incomplete market and takes quadratic utility function for our analysis. We firstly transform an incomplete market into complete one and derive the optimal investment and consumption strategy in the completed market by applying dynamic programming and Hamilton-Jacobi-Bellman(HJB) equation. Finally, a closed-form solution in an incomplete market is obtained according to the parameters relationship between the completed market and the original incomplete one.