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Application of a general risk management model to portfolio optimization problems with elliptical distributed returns for risk neutral and risk averse decision makers

Kaynar, Bahar and Birbil, Ş. İlker and Frenk, J.B.G. (2007) Application of a general risk management model to portfolio optimization problems with elliptical distributed returns for risk neutral and risk averse decision makers. [Working Paper / Technical Report] Sabanci University ID:SU_FENS_2007/0012

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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.

Item Type:Working Paper / Technical Report
Uncontrolled Keywords:Elliptical distributions; linear loss functions; value-at-risk; conditional value-at-risk; portfolio optimization; disutility
Subjects:H Social Sciences > HB Economic Theory
Q Science > QA Mathematics
ID Code:6300
Deposited By:İlker Şevket Birbil
Deposited On:24 Oct 2007 01:04
Last Modified:25 Oct 2007 12:26

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