The Probabilistic Risk Measure VaR as Constraint in Portfolio Optimization Problem-Reference-Cited by-同舟云学术

The Probabilistic Risk Measure VaR as Constraint in Portfolio Optimization Problem

Published:2021-03-01 Issue:1 Volume:21 Page:19-31
ISSN:1314-4081
Container-title:Cybernetics and Information Technologies
language:en
Short-container-title:

Author:

Stoilov Todor¹,Stoilova Krasimira¹,Vladimirov Miroslav²

Affiliation:

1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences , 1113 Sofia , Bulgaria

2. Varna University of Economics , 9002 Varna , Bulgaria

Abstract

Abstract The paper realizes inclusion of probabilistic measure for risk, VaR (Value at Risk), into a portfolio optimization problem. The formal analysis of the portfolio problem illustrates the evolution of the portfolio theory in sequentially inclusion of different market characteristics into the problem. They make modifications and complications of the portfolio problem by adding various constraints to consider requirements for taxes, boundaries for assets, cardinality constraints, and allocation of the investment resources. All these characteristics and parameters of the investment participate in the portfolio problem by analytical algebraic relations. The VaR definition of the portfolio risk is formalized in a probabilistic manner. The paper applies approximation of such probabilistic constraint in algebraic form. Geometrical interpretation is given for explaining the influence of the VaR constraint to the portfolio solution. Numerical simulation with data of the Bulgarian Stock Exchange illustrates the influence of the VaR constraint into the portfolio optimization problem.

Publisher

Walter de Gruyter GmbH

Subject

General Computer Science

Link

https://www.sciendo.com/pdf/10.2478/cait-2021-0002

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