Risk Measures and Portfolio Optimization

Portfolio Optimization with Higher Moment Risk Measures

The paper considers modeling of risk-averse preferences in stochastic programming problems using risk measures. We utilize the axiomatic foundation of coherent risk measures and deviation measures in order to develop simple representations that express risk measures via solutions of specially constructed stochastic programming problems. Using the developed representations, we introduce a new fa...

Portfolio Optimization with Quasiconvex Risk Measures

Polyhedral risk measures in electricity portfolio optimization

We compare different multiperiod risk measures taken from the class of polyhedral risk measures with respect to the effect they show when used in the objective of a stochastic program. For this purpose, simulation results of a stochastic programming model for optimizing the electricity portfolio of a German municipal power utility are presented and analyzed. This model aims to minimize risk and...

Fuzzy portfolio optimization under downside risk measures

This paper presents two fuzzy portfolio selection models where the objective is to minimize the downside risk constrained so that a given expected return should be achieved. We assume that the rates of returns on securities are approximated as LR-fuzzy numbers of the same shape, and that the expected return and risk are evaluated by interval-valued means. We establish the relationship between t...

Portfolio optimization with quantile-based risk measures

In this thesis we analyze Portfolio Optimization risk-reward theory, a generalization of the mean-variance theory, in the cases where the risk measures are quantile-based (such as the Value at Risk (V aR) and the shortfall). We show, using multicriteria theory arguments, that if the measure of risk is convex and the measure of reward concave with respect to the allocation vector, then the expec...