Download or read book Risk Capital Allocation by Coherent Risk Measures Based on One side Moments written by Tom Fischer and published by . This book was released on 2002 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Risk Capital Allocation by Coherent written by Tom Fischer and published by . This book was released on 2002 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Risk Measures and Capital Allocation written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This research first gives a review of risk measures and risk capital allocation, along with the important property of coherency, and the relationships between different coherent risk measures. Secondly, relative accuracy measures are used as model-based criteria to study whether or not bias adjustment by various bootstrap techniques could improve estimates of the expected shortfall (ES) as a risk measure. Thirdly, different tests for backtesting Value-at-Risk (VaR) and ES are investigated as data-based criteria of evaluating risk models. Fourthly, multivariate framework is developed for estimating (conditional) ES and ES risk contributions (ESC), as a principle of capital allocation. Finally, an empirical study of estimating ES and ESC with backtesting is carried out for historical data from Russell Indices.

Download or read book Modeling Measuring and Managing Risk written by Georg Ch Pflug and published by World Scientific. This book was released on 2007 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Risk Measures and Capital Allocation Principles for Risk Management written by Ying Wang and published by . This book was released on 2016 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk measures (or premium principles) and capital allocation principles play a signicant role in risk management. Regulators and companies in the financial markets usually adopt an appropriate risk measure, for example, Value-at-Risk (VaR) or Tail Value-at-Risk (TVaR), to determine the benchmarks. However, these risk measures are determined from the loss functions with constant weights, not random weight functions. This thesis proposes new approaches to determine risk measures from two perspectives. Firstly, we will generalize the definition of the tail subadditivity for distortion risk measures; we define the generalized GlueVaR (a linear combination of VaR and TVaRs) to approach any coherent distortion risk measure. Secondly, we will research the risk measures (or premium principles) and capital allocation principles based on the loss functions with random weight functions. The new reinsurance premium principles are derived similarly to the new risk measures. The two thresholds for the weight in the loss function can be employed by reinsurance companies as benchmarks when pricing the reinsurance products. The capital allocation principles derived based on the weighted loss functions are both mathematically and economically reasonable. Many of the risk measures and allocation principles, including the new risk measures, can be covered by this model. The results of this thesis have not only unified many of the risk measures and capital allocation principles, but also provided new and practical models.

Download or read book Advances in Finance and Stochastics written by Klaus Sandmann and published by Springer Science & Business Media. This book was released on 2002-04-23 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many areas of finance and stochastics, significant advances have been made since this field of research was opened by Black, Scholes and Merton in 1973. This volume contains a collection of original articles by a number of highly distinguished authors, on research topics that are currently in the focus of interest of both academics and practitioners.

Download or read book Capital Allocation La Aumann Shapley for Non Differentiable Risk Measures written by Francesca Centrone and published by . This book was released on 2017 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce a family of Capital allocation rules (C.A.R) based on the dual representation for risk measures and inspired to the Aumann-Shapley allocation principle. These rules extend the one of Denault and Kalkbrener (for coherent risk measures) and the one of Tsanakas (convex case), to the case of non Gateaux differentiable risk measures. We also study their properties and discuss their suitability in the quasiconvex context.

Download or read book Economic Capital Allocation Derived from Risk Measures written by Jan Dhaene and published by . This book was released on 2006 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: We examine properties of risk measures that can be considered to be in line with some quot;best practicequot; rules in insurance, based on solvency margins. We give ample motivation that all economic aspects related to an insurance portfolio should be considered in the definition of a risk measure. As a consequence, conditions arise for comparison as well as for addition of risk measures. We demonstrate that imposing properties that are generally valid for risk measures, in all possible dependency structures, based on the difference of the risk and the solvency margin, though providing opportunities to derive nice mathematical results, violates best practice rules. We show that so-called coherent risk measures lead to problems. In particular we consider an exponential risk measure related to a discrete ruin model, depending on the initial surplus, the desired ruin probability, and the risk distribution.

Download or read book Means and Their Inequalities written by P.S. Bullen and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't !hat they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal 0/ Fa/her 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van GuJik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fie1ds does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "complete1y integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing c1assification schemes. They draw upon wide1y different sections of mathematics.

Download or read book Capital Allocation for Set Valued Risk Measures written by Francesca Centrone and published by . This book was released on 2019 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce the notion of set-valued Capital Allocation rule, and study Capital allocation principles for multivariate set-valued coherent and convex risk measures. We compare these rules with some of those mostly used for univariate (single-valued) risk measures.

Download or read book Some Topics in Risk Theory and Optimal Capital Allocation Problems written by Binbin Liu and published by . This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Some Topics in Risk Theory and Optimal Capital Allocation Problems" by Binbin, Liu, 刘彬彬, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: In recent years, the Markov Regime-Switching model and the class of Archimedean copulas have been widely applied to a variety of finance-related fields. The Markov Regime-Switching model can reflect the reality that the underlying economy is changing over time. Archimedean copulas are one of the most popular classes of copulas because they have closed form expressions and have great flexibility in modeling different kinds of dependencies. In the thesis, we first consider a discrete-time risk process based on the compound binomial model with regime-switching. Some general recursive formulas of the expected penalty function have been obtained. The orderings of ruin probabilities are investigated. In particular, we show that if there exists a stochastic dominance relationship between random claims at different regimes, then we can order ruin probabilities under different initial regimes. Regarding capital allocation problems, which are important areas in finance and risk management, this thesis studies the problems of optimal allocation of policy limits and deductibles when the dependence structure among risks is modeled by an Archimedean copula. By employing the concept of arrangement increasing and stochastic dominance, useful qualitative results of the optimal allocations are obtained. Then we turn our attention to a new family of risk measures satisfying a set of proposed axioms, which includes the class of distortion risk measures with concave distortion functions. By minimizing the new risk measures, we consider the optimal allocation of policy limits and deductibles problems based on the assumption that for each risk there exists an indicator random variable which determines whether the risk occurs or not. Several sufficient conditions to order the optimal allocations are obtained using tools in stochastic dominance theory. DOI: 10.5353/th_b4819929 Subjects: Risk management - Mathematical models Investments - Mathematical models Portfolio management - Mathematical models

Download or read book Quantitative Portfolio Management written by Pierre Brugière and published by Springer Nature. This book was released on 2020-03-28 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book presents the main techniques of quantitative portfolio management and associated statistical methods in a very didactic and structured way, in a minimum number of pages. The concepts of investment portfolios, self-financing portfolios and absence of arbitrage opportunities are extensively used and enable the translation of all the mathematical concepts in an easily interpretable way. All the results, tested with Python programs, are demonstrated rigorously, often using geometric approaches for optimization problems and intrinsic approaches for statistical methods, leading to unusually short and elegant proofs. The statistical methods concern both parametric and non-parametric estimators and, to estimate the factors of a model, principal component analysis is explained. The presented Python code and web scraping techniques also make it possible to test the presented concepts on market data. This book will be useful for teaching Masters students and for professionals in asset management, and will be of interest to academics who want to explore a field in which they are not specialists. The ideal pre-requisites consist of undergraduate probability and statistics and a familiarity with linear algebra and matrix manipulation. Those who want to run the code will have to install Python on their pc, or alternatively can use Google Colab on the cloud. Professionals will need to have a quantitative background, being either portfolio managers or risk managers, or potentially quants wanting to double check their understanding of the subject.

Download or read book To Split or Not to Split written by Andreas Tsanakas and published by . This book was released on 2014 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex risk measures were introduced by Deprez and Gerber (1985). Here the problem of allocating risk capital to subportfolios is addressed, when aggregate capital is calculated by a convex risk measure. The Aumann-Shapley value is proposed as an appropriate allocation mechanism. Distortion-exponential measures are discussed extensively and explicit capital allocation formulas are obtained for the case that the risk measure belongs to this family. Finally the implications of capital allocation with a convex risk measure for the stability of portfolios are discussed.

Download or read book Risk Measures and Capital Allocation written by Chun-Ju Wang and published by . This book was released on 2010 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keywords: risk measures, capital allocation, conherency, VaR, expected shortfall, backtesting.

Download or read book Value at Risk and Bank Capital Management written by Francesco Saita and published by Elsevier. This book was released on 2010-07-26 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Value at Risk and Bank Capital Management offers a unique combination of concise, expert academic analysis of the latest technical VaR measures and their applications, and the practical realities of bank decision making about capital management and capital allocation. The book contains concise, expert analysis of the latest technical VaR measures but without the highly mathematical component of other books. It discusses practical applications of these measures in the real world of banking, focusing on effective decision making for capital management and allocation. The author, Francesco Saita, is based at Bocconi University in Milan, Italy, one of the foremost institutions for banking in Europe. He provides readers with his extensive academic and theoretical expertise combined with his practical and real-world understanding of bank structure, organizational constraints, and decision-making processes. This book is recommended for graduate students in master's or Ph.D. programs in finance/banking and bankers and risk managers involved in capital allocation and portfolio management. - Contains concise, expert analysis of the latest technical VaR measures but without the highly mathematical component of other books - Discusses practical applications of these measures in the real world of banking, focusing on effective decision making for capital management and allocation - Author is based at Bocconi University in Milan, Italy, one of the foremost institutions for banking in Europe

Download or read book Values of Non Atomic Games written by Robert J. Aumann and published by Princeton University Press. This book was released on 2015-03-08 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The "Shapley value" of a finite multi- person game associates to each player the amount he should be willing to pay to participate. This book extends the value concept to certain classes of non-atomic games, which are infinite-person games in which no individual player has significance. It is primarily a book of mathematics—a study of non-additive set functions and associated linear operators. Originally published in 1974. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Download or read book Geometry of Banach Spaces Selected Topics written by J. Diestel and published by Springer. This book was released on 2006-11-14 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: