Univariate and multivariate measures of risk aversion and risk premiums

Yuming Li and William T. Ziemba

Chapter 20 in Handbook of the Fundamentals of Financial Decision Making:In 2 Parts, 2013, pp 333-364 from World Scientific Publishing Co. Pte. Ltd.

Abstract: This paper develops univariate and multivariate measures of risk aversion for correlated risks. We derive Rubinstein's measures of risk aversion from the risk premiums with correlated random initial wealth and risk. It is shown that these measures are not only consistent with those for uncorrelated or independent risks, but also have the corresponding local properties of the Arrow-Pratt measures of risk aversion. Thus Rubinstein's measures of risk aversion are the appropriate extension of the Arrow-Pratt measures of risk aversion in the univariate case. We also derive a risk aversion matrix from the risk premiums with correlated initial wealth and risk vectors. This matrix measure is the multivariate version of Rubinstein's measures and is also the generalization of Duncan's results for non-random initial wealth. The univariate and multivariate measures of risk aversion developed in this paper are applied to portfolio theory in Li and Ziemba [15].

Keywords: Financial Decision Making; Asset Pricing; Prospect Theory; Utility Theory; Risk Aversion; Static Portfolio Theory; Stochastic Dominance; Dynamic Modeling; Dynamic Portfolio Theory; Tactical Asset Allocation; Kelly Strategy; Capital Growth (search for similar items in EconPapers)
Date: 2013
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