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Start Over Author "Zhang, Dali" Topic sample average approximation
5 results on '"Zhang, Dali"'

3. Confidence Levels for CVaR Risk Measures and Minimax Limits*

Author

Anderson, Edward, Xu, Huifu, and Zhang, Dali

Subjects
CVaR approximation, minimax, semi-infinate programming, sample average approximation, robust optimization, distributional robust optimization
Abstract

Conditional value at risk (CVaR) has been widely used as a risk measure in finance. When the confidence level of CVaR is set close to 1, the CVaR risk measure approximates the extreme (worst scenario) risk measure. In this paper, we present a quantitative analysis of the relationship between the two risk measures and it’s impact on optimal decision making when we wish to minimize the respective risk measures. We also investigate the difference between the optimal solutions to the two optimization problems with identical objective function but under constraints on the two risk measures. We discuss the benefits of a sample average approximation scheme for the CVaR constraints and investigate the convergence of the optimal solution obtained from this scheme as the sample size increases. We use some portfolio optimization problems to investigate teh performance of the CVaR approximation approach. Our numerical results demonstrate how reducing the confidence level can lead to a better overall performance.

Published
2014

4. Utility‐based shortfall risk: Efficient computations via Monte Carlo.

Author

Hu, Zhaolin and Zhang, Dali

Subjects
FINANCIAL risk management, FINANCIAL risk, MONTE Carlo method, ASYMPTOTIC normality, RISK managers
Abstract

With the development of financial risk management, the notion of convex risk measures has been proposed and has gained increasing attentions. Utility‐based shortfall risk (SR), as a specific and important class of convex risk measures, has become popular in recent years. In this paper we focus on the computational aspects of SR, which are significantly understudied but fundamental for risk assessment and management. We discuss efficient estimation, optimization, and sensitivity analysis of SR, based on Monte Carlo techniques and stochastic optimization methods. We also conduct extensive numerical studies on the proposed approaches. The numerical results further demonstrate the effectiveness of these approaches. [ABSTRACT FROM AUTHOR]

Published
2018
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5. Two-stage stochastic equilibrium problems with equilibrium constraints: modeling and numerical schemes.

Author

Zhang, Dali and Xu, Huifu

Subjects
*STOCHASTIC analysis, *CONSTRAINT satisfaction, *NUMERICAL analysis, *MONTE Carlo method, *STOCHASTIC convergence, *NASH equilibrium, *APPROXIMATION theory
Abstract

This article presents a two-stage stochastic equilibrium problem with equilibrium constraints (SEPEC) model. Some source problems which motivate the model are discussed. Monte Carlo sampling method is applied to solve the SEPEC. Convergence analysis on the statistical estimators of Nash equilibria and Nash stationary points are presented. [ABSTRACT FROM AUTHOR]

Published
2013
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