Some remarks on value-at-risk optimization

Some remarks on value-at-risk optimization∗

We discuss on observations related to value-at-risk optimization. Firstly, we consider a portfolio problem under an infinite number of value-at-risk inequality constraints (modeling first order stochastic dominance). The random data are assumed to be normally distributed. Although this problem is necessarily non-convex, an explicit solution can be derived. Secondly, we provide a (negative) resu...

Portfolio Optimization Based on Cross Efficiencies By Linear Model of Conditional Value at Risk Minimization

Markowitz model is the first modern formulation of portfolio optimization problem. Relyingon historical return of stocks as basic information and using variance as a risk measure aretow drawbacks of this model. Since Markowitz model has been presented, many effortshave been done to remove theses drawbacks. On one hand several better risk measures havebeen introduced and proper models have been ...

Value-at-Risk vs. Conditional Value-at-Risk in Risk Management and Optimization

From the mathematical perspective considered in this tutorial, risk management is a procedure for shaping a risk distribution. Popular functions managing risk are valueat-risk (VaR) and conditional value-at-risk (CVaR). The problem of choice between VaR and CVaR, especially in financial risk management, has been quite popular in academic literature. Reasons affecting the choice between VaR and ...

Optimization of Conditional Value-at-Risk

A new approach to optimizing or hedging a portfolio of nancial instruments to reduce risk is presented and tested on applications. It focuses on minimizing Conditional Value-at-Risk (CVaR) rather than minimizing Value-at-Risk (VaR), but portfolios with low CVaR necessarily have low VaR as well. CVaR, also called Mean Excess Loss, Mean Shortfall, or Tail VaR, is anyway considered to be a more co...

Value-at-Risk Based Portfolio Optimization