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Risk management with weighted VaR
Author(s) -
Wei Pengyu
Publication year - 2018
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12160
Subject(s) - expected shortfall , portfolio , value at risk , asset allocation , economics , risk measure , market risk , generalization , arbitrage , actuarial science , time consistency , spectral risk measure , risk management , selection (genetic algorithm) , expected utility hypothesis , class (philosophy) , value (mathematics) , asset (computer security) , econometrics , capital allocation line , microeconomics , financial economics , mathematics , computer science , finance , statistics , computer security , artificial intelligence , profit (economics) , mathematical analysis
This article studies the optimal portfolio selection of expected utility‐maximizing investors who must also manage their market‐risk exposures. The risk is measured by a so‐called weighted value‐at‐risk (WVaR) risk measure, which is a generalization of both value‐at‐risk (VaR) and expected shortfall (ES). The feasibility, well‐posedness, and existence of the optimal solution are examined. We obtain the optimal solution (when it exists) and show how risk measures change asset allocation patterns. In particular, we characterize three classes of risk measures: the first class will lead to models that do not admit an optimal solution, the second class can give rise to endogenous portfolio insurance, and the third class, which includes VaR and ES, two popular regulatory risk measures, will allow economic agents to engage in “regulatory capital arbitrage,” incurring larger losses when losses occur.