An optimal consumption and investment problem with quadratic utility and negative wealth constraints

[摘要] In this paper, we investigate the optimal consumption and portfolio selection problem with negative wealth constraints for an economic agent who has a quadratic utility function of consumption and receives a constant labor income. Due to the property of the quadratic utility function, we separate our problem into two cases and derive the closed-form solutions for each case. We also illustrate some numerical implications of the optimal consumption and portfolio.

[学科分类] 数学（综合）

[关键词] consumption;portfolio selection;quadratic utility;negative wealth constraints;martingale method