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- Article name
- OPTIMALITY CONDITIONS FOR A ONE-STAGE OPTIMIZATION PORTFOLIO PROBLEM UNDER A VALUE AT RISK CONSTRAINT ON INVESTOR'S CAPITAL
- Authors
- Golubin A. Yu., , info@ditc.ras.ru, Design Information Technologies Center of the RAS; National Research University Higher School of Economics, Odintsovo, Moscow region, Russia; Moscow, Russia
Gazov A. I., , info@ditc.ras.ru, Design Information Technologies Center of the RAS, Odintsovo, Moscow region, Russia
- Keywords
- portfolio optimization / value at risk constraint / dual cone
- Year
- 2018 Issue 4 Pages 53 - 57
- Code EDN
- Code DOI
- Abstract
- The present paper studies a portfolio optimization problem with a value at risk (VaR) constraint that imposes a boundary for probability of the investor's capital shortfall. In terms of Lagrange function and the dual to a cone generated by the VaR constraint, we find in an explicit form necessary and sufficient conditions for: non-emptiness of the set of admissible points, the fulfillment of Slater's regularity condition, and optimality in the optimization problem. The existence and uniqueness of a solution are also studied.
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