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.

Additional Metadata
Keywords Conditional value-at-risk, Disutility, Elliptical distributions, Linear loss functions, Portfolio optimization, Value-at-risk
Publisher Erasmus Research Institute of Management (ERIM)
Persistent URL hdl.handle.net/1765/10151
Citation
Kaynar, B, Birbil, S.I, & 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 (No. ERS-2007-032-LIS). ERIM report series research in management Erasmus Research Institute of Management. Erasmus Research Institute of Management (ERIM). Retrieved from http://hdl.handle.net/1765/10151