Risk-Aversion Behavior in Consumption/Investment Problems with Subsistence Consumption

Abstract

In this chapter we study the risk-aversion behavior of an agent in the dynamic framework of consumption/investment decision making that allows the presence of a subsistence consumption level and the possibility of bankruptcy. Agent’s consumption utility is assumed to be represented by a strictly increasing, strictly concave, continuously differentiable function in the general case and by a HARA type function in the special case treated in the chapter. Coefficients of absolute and relative risk aversion are defined to be the well-known curvature measures associated with the derived utility of wealth obtained as the value function of the agent’s optimization problem. In the HARA case the agent’s absolute risk aversion decreases with wealth if his wealth is greater than some boundary level, while at lower wealth levels it increases with wealth. We describe the dependence of this boundary on the value assigned to bankruptcy. Furthermore, the agent’s relative risk aversion in the HARA case inherits the monotonicity behavior from his consumption utility provided his wealth is greater than another boundary level. At smaller wealth levels, however, the relative risk aversion is increasing not only in the HARA case, but also in the general case. Finally, in the HARA case we describe the agent’s optimal investment policy in terms of his wealth for different values of problem parameters.