Risk-Aversion Behavior in Consumption/Investment Problems

Posted: 15 Jan 2008 Last revised: 31 Jan 2019

See all articles by Ernst Presman

Ernst Presman

Russian Academy of Sciences (RAS)

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

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Abstract

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.

Keywords: Risk Aversion, investment-consumption problem, consumption/portfolio problem, dynamic programming, stochastic control, bankruptcy

JEL Classification: G11, C61

Suggested Citation

Presman, Ernst and Sethi, Suresh, Risk-Aversion Behavior in Consumption/Investment Problems. Mathematical Finance, Vol. 1, No. 1, pp. 100-124, January 1991 , Available at SSRN: https://ssrn.com/abstract=1083195

Ernst Presman

Russian Academy of Sciences (RAS) ( email )

Leninsky Ave, 14
Moscow, 119991
Russia

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

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