Risk-Aversion Behavior in Consumption/Investment Problems

In this paper, we study the risk-aversion behavior of an agent in the dynamic framework of consumption/investment decision making that allows 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 paper. 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. Through an analysis of these coefficients, we show how the change in agent's risk aversion as his wealth changes depends on his consumption utility and the other problem parameters, including the payment at bankruptcy. Moreover, in the HARA case, we can conclude that the agent's relative risk aversion is nondecreasing with wealth, while his absolute risk aversion is decreasing with wealth only if he is sufficiently wealthy. At lower wealth levels, however, the agent's absolute risk aversion may increase with wealth in some cases