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

Convex Analysisの二,三の進展について

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

This article characterizes the systematic risk exposures of hedge funds using buy-and-hold and option-based strategies. Our results show that a large number of equity-oriented hedge fund strategies exhibit payoffs resembling a short position in a put option on the market index and therefore bear significant left-tail risk, risk that is ignored by the commonly used mean-variance framework. Using a mean-conditional value-at-risk framework, we demonstrate the extent to which the mean-variance framework underestimates the tail risk. Finally, working with the systematic risk exposures of hedge funds, we show that their recent performance appears significantly better than their long-run performance. It is well accepted that the world of financial securities is a multifactor world consisting of different risk factors, each associated with its own factor risk premium, and that no single investment strategy can span the entire ‘‘risk factor space.’’ Therefore investors wishing to earn risk premia associated with different risk factors need to employ different kinds of investment strategies. Sophisticated investors, like endowments and pension funds, seem to have recognized this fact as their portfolios consist

/pdf/risks-and-portfolio-decisions-involving-hedge-funds-3ddeaoadsv.pdf

Risks and Portfolio Decisions Involving Hedge Funds

This article has outlined a new approach for the simultaneous calculation of value-at-risk (VaR) and optimization of conditional VaR (CVaR) for a broad class of problems. We have shown that CVaR can be efficiently minimized using LP techniques. Our numerical experiments show that CVaR optimal portfolios are near optimal in VaR terms, i.e., VaR cannot be reduced further more than a few percent. Also, CVaR constraints can be handled efficiently using equivalent linear constraints, which dramatically improves the efficiency of the optimization techniques.

Conditional value-at-risk: optimization algorithms and applications

In this paper, we analyze the portfolio selection implications arising from imposing a value-at-risk (VaR) constraint on the mean-variance model, and compare them with those arising from the imposition of a conditional value-at-risk (CVaR) constraint. We show that for a given confidence level, a CVaR constraint is tighter than a VaR constraint if the CVaR and VaR bounds coincide. Consequently, a CVaR constraint is more effective than a VaR constraint as a tool to control slightly risk-averse agents, but in the absence of a risk-free security, has a perverse effect in that it is more likely to force highly risk-averse agents to select portfolios with larger standard deviations. However, when the CVaR bound is appropriately larger than the VaR bound or when a risk-free security is present, a CVaR constraint "dominates" a VaR constraint as a risk management tool.

https://www.jstor.org/stable/pdfplus/30046232.pdf

A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model

Recently, a new approach for optimization of Conditional Value-at-Risk (CVaR) was suggested and tested with several applications. For continuous distributions, CVaR is defined as the expected loss exceeding Value-at Risk (VaR). However, generally, CVaR is the weighted average of VaR and losses exceeding VaR. Central to the approach is an optimization technique for calculating VaR and optimizing CVaR simultaneously. This paper extends this approach to the optimization problems with CVaR constraints. In particular, the approach can be used for maximizing expected returns under CVaR constraints. Multiple CVaR constraints with various confidence levels can be used to shape the profit/loss distribution. A case study for the portfolio of S&P 100 stocks is performed to demonstrate how the new optimization techniques can be implemented.

/pdf/portfolio-optimization-with-conditional-value-at-risk-3xygs1o3t8.pdf

Jonas Palmquist

Papers

Portfolio optimization with conditional value-at-risk objective and constraints