Application of a General Risk Management Model to Portfolio Optimization Problems with Elliptical Distributed Returns for Risk Neutral and Risk Averse Decision Makers
2007-05-24
Research Paper
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Published by
Rotterdam School of Management (RSM) Erasmus University, Erasmus Research Institute of Management (ERIM)
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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
Classifications using
Journal of Economic Literature (JEL) Classification System
- C61 : Optimization Techniques; Programming Models; Dynamic Analysis
- G3 : Corporate Finance and Governance
- M11 : Production Management
- M : Business Administration and Business Economics; Marketing; Accounting
- G11 : Portfolio Choice; Investment Decisions
Automatically Extracted Terms
- function
- distribution
- decision maker
- problem
- measure
- decision
- maker
- disutility
- value
- risk measure
- disutility function
- algorithm
- portfolio
- lemma
- disutility functions
- vector
- decision makers
- optimization
- return
- result
