This paper examines a new approach for credit risk optimization. The model is based on the Conditional Value-at-Risk (CVaR) risk measure, the expected loss exceeding Value-at-Risk. CVaR is also known as Mean Excess, Mean Shortfall, or Tail VaR. This model can simultaneously adjust all positions in a portfolio of financial instruments in order to minimize CVaR subject to trading and return const...

This paper describes a way how to find the minimal seller’s price for a unit-linked insurance product in order to make the claim acceptable, under the assumption that information about the insurance process is only available at the time of maturity. For the general case, the price calculated here provides still an upper bound. Acceptability is defined through the CVaR criterion. Furthermore, th...

Recognizing the drawbacks of Value-at-Risk (VaR), researchers have advocated the use of Conditional Value-at-Risk (CVaR). However, the current popularity of VaR and Stress Testing (ST) among bank regulators raises the question of whether a risk management system based on both VaR and ST constraints is an effective alternative to a system based on CVaR. We show that when the VaR and ST bounds ar...

Multi-asset class (MAC) portfolios can be comprised of investments in equities, fixed-income, commodities, foreign-exchange, credit, derivatives, and alternatives such as real-estate and private equity. The return for such non-linear portfolios is asymmetric with significant tail risk. The traditional Markowitz Mean-Variance Optimization (MVO) framework, that linearizes all the assets in the po...

Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR) are two risk measures which are widely used in the practice of risk management. This paper deals with the problem of estimating both VaR and CVaR using stochastic approximation (with decreasing steps): we propose a first Robbins-Monro (RM) procedure based on Rockafellar-Uryasev’s identity for the CVaR. Convergence rate of this algorithm t...

Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) are two risk measures which are widely used in the practice of risk management. This paper deals with the problem of computing both VaR and CVaR using stochastic approximation (with decreasing steps): we propose a first Robbins-Monro procedure based on Rockaffelar-Uryasev’s identity for the CVaR. The convergence rate of this algorithm to ...

This paper investigates a risk-averse inventory model by balancing the expected profit and conditional value-at-risk (CVaR) in a newsvendor model setting. We find out that: i) The optimal order quantity is increasing in the shortage cost for both the CVaR only criterion and the tradeoff objective. ii) For the case of zero shortage cost, the optimal order quantity to the CVaR criterion or tradeo...

This note is focused on computational efficiency of the portfolio selection models based on the Conditional Value at Risk (CVaR) risk measure. The CVaR measure represents the mean shortfall at a specified confidence level and its optimization may be expressed with a Linear Programming (LP) model. The corresponding portfolio selection models can be solved with general purpose LP solvers. However...