https://link.springer.com/content/pdf/10.2307%2F3343168.pdf

Development as Freedom

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

From the Publisher:
Pattern recognition has long been studied in relation to many different (and mainly unrelated) applications, such as remote sensing, computer vision, space research, and medical imaging. In this book Professor Ripley brings together two crucial ideas in pattern recognition; statistical methods and machine learning via neural networks. Unifying principles are brought to the fore, and the author gives an overview of the state of the subject. Many examples are included to illustrate real problems in pattern recognition and how to overcome them.This is a self-contained account, ideal both as an introduction for non-specialists readers, and also as a handbook for the more expert reader.

Pattern recognition and neural networks

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

Preface * Introduction * The Bayes Error * Inequalities and alternatedistance measures * Linear discrimination * Nearest neighbor rules *Consistency * Slow rates of convergence Error estimation * The regularhistogram rule * Kernel rules Consistency of the k-nearest neighborrule * Vapnik-Chervonenkis theory * Combinatorial aspects of Vapnik-Chervonenkis theory * Lower bounds for empirical classifier selection* The maximum likelihood principle * Parametric classification *Generalized linear discrimination * Complexity regularization *Condensed and edited nearest neighbor rules * Tree classifiers * Data-dependent partitioning * Splitting the data * The resubstitutionestimate * Deleted estimates of the error probability * Automatickernel rules * Automatic nearest neighbor rules * Hypercubes anddiscrete spaces * Epsilon entropy and totally bounded sets * Uniformlaws of large numbers * Neural networks * Other error estimates *Feature extraction * Appendix * Notation * References * Index

/pdf/a-probabilistic-theory-of-pattern-recognition-1p19dg485x.pdf

A Probabilistic Theory of Pattern Recognition

The value-at-risk (VaR) and the conditional value-at-risk (CVaR) are two commonly used risk measures. We state some of their properties and make a comparison. Moreover, the structure of the portfolio optimization problem using the VaR and CVaR objective is studied.

Some Remarks on the Value-at-Risk and the Conditional Value-at-Risk

An assessment of economic flood risk trends across Europe reveals high current and future stress on risk financing schemes. The magnitude and distribution of losses can be contained by investing in flood protection, increasing insurance coverage or by expanding public compensation funds. However, these climate change adaptation instruments have vastly different efficiency, equity and acceptability implications. Moreover, the spatial variation in disaster risk can necessitate cross-subsidies between individual countries in the European Union.

Increasing stress on disaster-risk finance due to large floods

This book is the first in the market to treat single- and multi-period risk measures (risk functionals) in a thorough, comprehensive manner. It combines the treatment of properties of the risk measures with the related aspects of decision making under risk. 



The book introduces the theory of risk measures in a mathematically sound way. It contains properties, characterizations and representations of risk functionals for single-period and multi-period activities, and also shows the embedding of such functionals in decision models and the properties of these models.

Modeling, Measuring and Managing Risk

A stochastic branch and bound method for solving stochastic global optimization problems is proposed. As in the deterministic case, the feasible set is partitioned into compact subsets. To guide the partitioning process the method uses stochastic upper and lower estimates of the optimal value of the objective function in each subset. Convergence of the method is proved and random accuracy estimates derived. Methods for constructing stochastic upper and lower bounds are discussed. The theoretical considerations are illustrated with an example of a facility location problem.

/pdf/a-branch-and-bound-method-for-stochastic-global-optimization-xy4xk63iy1.pdf

A branch and bound method for stochastic global optimization

Value-at-Risk (VAR) is an important and widely used measure of the extent to which a given portfolio is subject to risk present in financial markets. In this paper, we present a method of calculating a portfolio that gives the optimal VAR among those which yield at least some specified expected return. This method allows us to calculate the mean-VAR-efficient frontier. The method is based on the approximation of historical VAR by smoothed VAR (SVAR), which filters out local irregular behavior of the historical VAR function. Moreover, we compare VAR as a risk measure to other well-known measures of risk, such as conditional value-at risk (CVAR) and the standard deviation. We show that the resulting efficient frontiers are quite different. An investor who wants to controls his or her VAR should not look at portfolios lying on other than the VAR efficient frontier, although the calculation of this frontier is algorithmically more complex than other frontiers. We support this conjecture by presenting the results of a large-scale experiment with a representative selection of stock and bond indices from developed and emerging markets that involved the computation of many thousand VAR-optimal portfolios.

Georg Ch. Pflug

Papers

Some Remarks on the Value-at-Risk and the Conditional Value-at-Risk

Increasing stress on disaster-risk finance due to large floods

Modeling, Measuring and Managing Risk

A branch and bound method for stochastic global optimization

Value-at-Risk in Portfolio Optimization: Properties and Computational Approach