The dependence of the incremental risk rate of interest on absolute risk aversion - Applying the Laplace transform to risk preference evaluation

Abstract

In this paper we base our study on the application of the Laplace transform to risk preference theory. With a constant measure of absolute risk aversion (Pratt, 1964; Arrow, 1965), the Certainty Monetary Equivalent (CME) of a risky project previously has been developed into an expression involving the logarithm of the bilateral Laplace transform of the probability density of its stochastic economic outcome. The internal risk aversion (IRA) is the break-even level of the absolute risk aversion, between making the project favourable or unfavourable.Below, we apply this methodology to determining an expression for the incremental risk rate of interest in the case of standard investments with payments having probability distributions. A simple approximate formula is derived explaining how the incremental risk rate of interest depends on the absolute risk aversion and the discount rate, i.e. on measures of risk preference and of time preference.