25 research outputs found
A second-order stochastic dominance portfolio efficiency measure
summary:In this paper, we introduce a new linear programming second-order stochastic dominance (SSD) portfolio efficiency test for portfolios with scenario approach for distribution of outcomes and a new SSD portfolio inefficiency measure. The test utilizes the relationship between CVaR and dual second-order stochastic dominance, and contrary to tests in Post [Post] and Kuosmanen [Kuosmanen], our test detects a dominating portfolio which is SSD efficient. We derive also a necessary condition for SSD efficiency using convexity property of CVaR to speed up the computation. The efficiency measure represents a distance between the tested portfolio and its least risky dominating SSD efficient portfolio. We show that this measure is consistent with the second-order stochastic dominance relation. We find out that this measure is convex and we use this result to describe the set of SSD efficient portfolios. Finally, we illustrate our results on a numerical example
Efficiency analysis of several EU stock markets: mean-risk efficient portfolios
Web of Science29571069
Contractivity of Bellman Operator in Risk Averse Dynamic Programming with Infinite Horizon
The paper deals with a risk averse dynamic programming problem with infinite
horizon. First, the required assumptions are formulated to have the problem
well defined. Then the Bellman equation is derived, which may be also seen as a
standalone reinforcement learning problem. The fact that the Bellman operator
is contraction is proved, guaranteeing convergence of various solution
algorithms used for dynamic programming as well as reinforcement learning
problems, which we demonstrate on the value iteration algorithm
Value at Risk application to FSD portfolio efficiency testing
The paper deals with efficiency testing of a given portfolio with respect to all other portfolios that can be created from the considered set of assets. The efficiency is based on the first order stochastic dominance (FSD) relation. A necessary and sufficient condition for the first order stochastic dominance criterion is expressed in terms of Value at Risks (VaRs). Consequently a FSD portfolio efficiency test based on VaRs is formulated. Contrary to the usual case, a general discrete distribution of portfolio returns is assumed what makes the test computationally more demanding comparing to the equiprobable scenarios case. Therefore we present a tractable reformulation of this test that turns constraints on VaRs into classical mixed-integer nonlinear programming problem
Užitkové funkce v úlohách optimalizace portfolia
Katedra pravděpodobnosti a matematické statistikyDepartment of Probability and Mathematical StatisticsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult
Value at Risk application to FSD portfolio efficiency testing
Abstract The paper deals with efficiency testing of a given portfolio with respect to all other portfolios that can be created from the considered set of assets. The efficiency is based on the first order stochastic dominance (FSD) relation. A necessary and sufficient condition for the first order stochastic dominance criterion is expressed in terms of Value at Risks (VaRs). Consequently a FSD portfolio efficiency test based on VaRs is formulated. Contrary to the usual case, a general discrete distribution of portfolio returns is assumed what makes the test computationally more demanding comparing to the equiprobable scenarios case. Therefore we present a tractable reformulation of this test that turns constraints on VaRs into classical mixed-integer nonlinear programming problem
Stabilita SSD eficience portfolia - měsíční versus roční výnosy
Stability of SSD portfolio efficiency - monthly versus yearly returns