This study is concerned with the dynamic risk-analysis for finite state Markov decision processes. As a measure of risk, we consider conditional value-at-risk(CVaR) for the real value of the discounted total reward from a policy, under whose criterion risk optimal or deterministic policies are defined. The risk problem is equivalently redefined as a non-linear optimization problem on the attain...

The size of banks is examined as a determinant of bank risk. A wide range of banks are examined across four regions, including Australia, Canada, Europe and the USA. Four risk metrics are considered including Value at Risk (VaR), Conditional Value at Risk (CVaR, which measures risk beyond VaR), Probability of Default (PD) using Merton structural methodology, and Conditional Probability of Defau...

We study profit maximization vs risk approaches for the standard newsvendor problemwith uncertainty in demand as well as a generalized version with uncertainty in the shortage cost (as often applies in practice). We consider two well-known risk approaches: Value-at-Risk (VaR) included as a constraint and Conditional Value-at-Risk (CVaR). We first derive the explicit expressions of the optimal s...

Motivated by viral marketing, stochastic diffusion processes that model influence spread on a network have been studied intensively. The primary interest in such models has been to find a seed set of a fixed size that maximizes the expected size of the cascade from it. Practically, however, it is not desirable to have the risk of ending with a small cascade, even if the expected size of the cas...

Motivated by the progress made towards incorporating robust optimization in framework of risk minimization, this work focuses on assessing practical usefulness approaches for minimization downside measures, such as Value-at-Risk (VaR) and Conditional (CVaR). Accordingly, we perform empirical analysis performance VaR CVaR models with respect to their counterparts, namely, Worst-Case CVaR, using ...

We model the new quantitative aspects of market risk management for banks that Basel established in 2016 and came into effect January 2019. Market is measured by Conditional Value at Risk (CVaR) or Expected Shortfall a confidence level 97.5%. The regulatory backtest remains largely based on 99% VaR. As additional statistical procedures, line with recommendations, supplementary VaR CVaR backtest...

The use of derivatives can lead to higher yields and lower funding costs. In addition, derivatives are indispensable tools for risk management. We analyze the derivative portfolio hedging problems based on value at risk (VaR) and conditional value at risk (CVaR). We show that these derivative portfolio optimization problems are often ill-posed and the resulting optimal portfolios frequently inc...

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 ...

Goal achieving is a commonly observed phenomenon in practice, and it plays an important role in decision making. In this paper we investigate the impact of a target on newsvendor decisions. We take into account the risk and model the effect of a target by maximizing the satisficing measure of a newsvendor’s profit with respect to that target. We study two satisficing measures: i) CVaR (Conditio...

This paper proposes the portfolio stochastic programming (PSP) model and the stagewise portfolio stochastic programming (SPSP) model for investing in stocks in the Taiwan stock market. The SPSP model effectively reduces the computational resources needed to solve the PSP model. Additionally, the conditional value at risk (CVaR) is used as a risk measure in the models. In each period of investme...