/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

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 consistent measure of risk than VaR. Central to the new approach is a technique for portfolio optimization which calculates VaR and optimizes CVaR simultaneously. This technique is suitable for use by investment companies, brokerage rms, mutual funds, and any business that evaluates risks. It can be combined with analytical or scenario-based methods to optimize portfolios with large numbers of instruments, in which case the calculations often come down to linear programming or nonsmooth programming. The methodology can be applied also to the optimization of percentiles in contexts outside of nance.

/pdf/optimization-of-conditional-value-at-risk-338oy3ddeu.pdf

Optimization of conditional value-at-risk

Fundamental properties of conditional value-at-risk (CVaR), as a measure of risk with significant advantages over value-at-risk (VaR), are derived for loss distributions in finance that can involve discreetness. Such distributions are of particular importance in applications because of the prevalence of models based on scenarios and finite sampling. CVaR is able to quantify dangers beyond VaR and moreover it is coherent. It provides optimization short-cuts which, through linear programming techniques, make practical many large-scale calculations that could otherwise be out of reach. The numerical efficiency and stability of such calculations, shown in several case studies, are illustrated further with an example of index tracking.

/pdf/conditional-value-at-risk-for-general-loss-distributions-4789km634z.pdf

Conditional value-at-risk for general loss distributions

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

This book provides the most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management. Whether you are a financial risk analyst, actuary, regulator or student of quantitative finance, Quantitative Risk Management gives you the practical tools you need to solve real-world problems. Describing the latest advances in the field, Quantitative Risk Management covers the methods for market, credit and operational risk modelling. It places standard industry approaches on a more formal footing and explores key concepts such as loss distributions, risk measures and risk aggregation and allocation principles. The book's methodology draws on diverse quantitative disciplines, from mathematical finance and statistics to econometrics and actuarial mathematics. A primary theme throughout is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. Proven in the classroom, the book also covers advanced topics like credit derivatives. Fully revised and expanded to reflect developments in the field since the financial crisis Features shorter chapters to facilitate teaching and learning Provides enhanced coverage of Solvency II and insurance risk management and extended treatment of credit risk, including counterparty credit risk and CDO pricing Includes a new chapter on market risk and new material on risk measures and risk aggregation

/pdf/quantitative-risk-management-concepts-techniques-and-tools-afazrwn4wm.pdf

Quantitative Risk Management: Concepts, Techniques, and Tools

Fundamental properties of conditional value-at-risk, as a measure of risk with significant advantages over value-at-risk, are derived for loss distributions in finance that can involve discreetness. Such distributions are of particular importance in applications because of the prevalence of models based on scenarios and finite sampling. Conditional value-at-risk is able to quantify dangers beyond value-at-risk, and moreover it is coherent. It provides optimization shortcuts which, through linear programming techniques, make practical many large-scale calculations that could otherwise be out of reach. The numerical efficiency and stability of such calculations, shown in several case studies, are illustrated further with an example of index tracking.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID267256_code010418130.pdf?abstractid=267256&type=2

Conditional Value-at-Risk for General Loss Distributions

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 constraints. The credit risk distribution is generated by Monte Carlo simulations and the optimization problem is solved effectively by linear programming. The algorithm is very efficient; it can handle hundreds of instruments and thousands of scenarios in reasonable computer time. The approach is demonstrated with a portfolio of emerging market bonds.

/pdf/credit-risk-optimization-with-conditional-value-at-risk-3q8bgy1xwa.pdf

Credit risk optimization with Conditional Value-at-Risk criterion

Preface. Introduction to the Theory of Probabilistic Functions and Percentiles S. Uryasev. Pricing American Options by Simulation Using a Stochastic Mesh with Optimized Weights M. Broadie, et al. On Optimization of Unreliable Material Flow Systems Y. Ermoliev, et al. Stochastic Optimization in Asset & Liability Management: A Model for Non-Maturing Accounts K. Frauendorfer, M. Schurle. Optimization in the Space of Distribution Functions and Applications in the Bayes Analysis A.N. Golodnikov, et al. Sensitivity Analysis of Worst-Case Distribution for Probability Optimization Problems Y.S. Kan, A.I. Kibzun. On Maximum Realiability Problem in Parallel-Series Systems with Two Failure Modes V. Kirilyuk. Robust Monte Carlo Simulation for Approximate Covariance Matrices and VaR Analyses A. Kreinin, A. Levin. Structure of Optimal Stopping Strategies for American Type Options A.G. Kukush, D.S. Silvestrov. Approximation of Value-at-Risk Problems with Decision Rules R. Lepp. Managing Risk with Expected Shortfall H. Mausser, D. Rosen. On the Numerical Solution of Jointly Chance Constrained Problems J. Mayer. Management of Quality of Service through Chance-constraints in Multimedia Networks E.A. Medova, J.E. Scott. Solution of a Product Substitution Problem Using Stochastic Programming M.R. Murr, A. Prekopa. Some Remarks on the Value-at-Risk and the Conditional Value-at-risk G.Ch. Pflug. Statistical Inference of Stochastic Optimization Problems A. Shapiro.

Probabilistic constrained optimization : methodology and applications

A new one-parameter family of risk measures called Conditional Drawdown (CDD) has been proposed. These measures of risk are functionals of the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter Alpha, in the case of a single sample path, drawdown functional is defined as the mean of the worst (1 - Alpha) 100% drawdowns. The CDD measure generalizes the notion of the drawdown functional to a multi-scenario case and can be considered as a generalization of deviation measure to a dynamic case. The CDD measure includes the Maximal Drawdown and Average Drawdown as its limiting cases. Mathematical properties of the CDD measure have been studied and efficient optimization techniques for CDD computation and solving asset-allocation problems with a CDD measure have been developed. The CDD family of risk functionals is similar to Conditional Value-at-Risk (CVaR), which is also called Mean Shortfall, Mean Excess Loss, or Tail Value-at-Risk. Some recommendations on how to select the optimal risk functionals for getting practically stable portfolios have been provided. A real-life asset-allocation problem has been solved using the proposed measures. For this particular example, the optimal portfolios for cases of Maximal Drawdown, Average Drawdown, and several intermediate cases between these two have been found.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID544742_code375170.pdf?abstractid=544742&mirid=1

Stanislav Uryasev

Papers

Conditional value-at-risk for general loss distributions

Conditional Value-at-Risk for General Loss Distributions

Credit risk optimization with Conditional Value-at-Risk criterion

Probabilistic constrained optimization : methodology and applications

Drawdown Measure in Portfolio Optimization