Application of a General Risk Management Model to Portfolio Optimization Problems with Elliptical Distributed Returns for Risk Neutral and Risk Averse Decision Makers

B. Kaynar, Ilker Birbil and Hans Frenk

ERIM Report Series Research in Management from Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam

Abstract: In this paper portfolio problems with linear loss functions and multivariate elliptical distributed returns are studied. We consider two risk measures, Value-at-Risk and Conditional-Value-at-Risk, and two types of decision makers, risk neutral and risk averse. For Value-at-Risk, we show that the optimal solution does not change with the type of decision maker. However, this observation is not true for Conditional-Value-at-Risk. We then show for Conditional-Value-at-Risk that the objective function can be approximated by Monte Carlo simulation using only a univariate distribution. To solve the equivalent Markowitz model, we modify and implement a finite step algorithm. Finally, a numerical study is conducted.

Keywords: Conditional value-at-risk; Disutility; Elliptical distributions; Linear loss functions; Portfolio optimization; Value-at-risk (search for similar items in EconPapers)
JEL-codes: C61 G11 G3 M M11 (search for similar items in EconPapers)
Date: 2007-05-24
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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