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 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 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 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 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 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 Internal Credit Risk Models written by Michael K. Ong and published by Risk Publications. This book was released on 1999 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical, accessible step-by-step analysis of the theory and practicalities of credit risk measurement and management.

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 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 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 Risk Quantification and Allocation Methods for Practitioners written by Montserrat Guillén and published by Amsterdam University Press. This book was released on 2018-01-23 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk Quantification and Allocation Methods for Practitioners offers a practical approach to risk management in the financial industry. This in-depth study provides quantitative tools to better describe qualitative issues, as well as clear explanations of how to transform recent theoretical developments into computational practice, and key tools for dealing with the issues of risk measurement and capital allocation.

Download or read book Value Oriented Risk Management of Insurance Companies written by Marcus Kriele and published by Springer Science & Business Media. This book was released on 2014-01-14 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Value- and risk-oriented management is a holistic method of managing businesses. In this book both actuarial methods and methods pertaining to classical internal control and classical risk management are used. Therefore the approach taken is necessarily interdisciplinary. Indeed, there is a new dynamically developing field for actuaries as a result of the emphasis now on the measurement of risk. This book provides the required basic knowledge for this subject from an actuarial perspective. It enables the reader to implement in practice a risk management system that is based on quantitative methods. With this book, the reader will additionally be able to critically appraise the applicability and the limits of the methods used in modern risk management. Value-oriented Management of Risk in Insurance focuses on risk capital, capital allocation, performance measurement and value-oriented management. It also makes a connection to regulatory developments (for example, Solvency II). The reader should have a basic knowledge of probability and familiarity with mathematical concepts. It is intended for working actuaries and quantitative risk managers as well as actuarial students.

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 Capital Allocation in Financial Institutions written by Dóra Balog and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Capital allocation is used for many purposes in financial institutions and for this purpose several methods are known. The aim of this paper is to review possible methods (we present six of them) and to help financial companies to choose between the methods. There are some properties that an allocation method should satisfy: full allocation, core compatibility, riskless allocation, symmetry and suitability for performance measurement (compatibility with Return on Risk Adjusted Capital calculation). If we think about practical application we should also consider simplicity of the methods. First we examine the methods from the point of view if they are satisfying core compatibility. We test this with simulation where we add to the existing literature that we test core compatibility with different assumptions on returns: on normal and t-distributed returns and also on returns generated from a copula. We find that if we measure risk by a coherent risk measure, the Expected Shortfall there are two methods satisfying core compatibility: the Euler method (that always fulfills the criteria) and cost gap method (obeys it around in about 99%). As Euler method is very easy to calculate even for many players while cost gap method becomes very complicated as the number of the players increases we examine further the properties of Euler method. We find that it fulfills all the above given criteria but symmetry and as aforementioned it is also very easy to calculate. Therefore we believe that the method might be suggested for practical applications. -- Capital Allocation ; Coherent Measures of Risk ; Core ; Simulation

Download or read book Statistical Issues in Coherent Risk Management written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Measuring risk is a crucial aspect of the portfolio optimization problem in finance, and of capital adequacy assessment in risk management. Expected Shortfall (ES) has been proposed as a coherent risk measure, by contrast with Value-at-Risk (VaR) and the standard-deviation-type of measures. Based on a coherent risk measure, for instance ES, we can discuss a coherent capital allocation for the purpose of internal risk management and performance measure, if ES is used for economic capital held by financial firms as a cushion to absorb the unexpected losses. Properly allocating risk capital down to the business level is important for the purpose of risk management and portfolio performance measurement. Even if there is a doubt about the reason for allocating ES, instead of VaR, the statistical properties of the statistic, marginal ES, from the proposed coherent allocation rule, are still of interest, because it is exactly the sensitivity of the target portfolio's ES. The idea of a coherent capital allocation rule by using a cost sharing rule, the Aumann-Shapley value in game theory, proposed by Denault (2001), happens to result in the same formula as proposed by Tasche (2000), who independently develops the "suitable" allocation rule based on the discussion of risk-adjusted returns. The fact, that two aspects of the concerns are satisfied by the same allocation formula, brings two fields together in an integrated way, so that a systematic risk management in a banking system seems very promising. Fundamental statistical issues arise in several places in a coherent risk management system. Primary interests will be, and are always, in modeling the profit/loss (P/L) distributions. Statistical modeling is receiving more and more attention currently, as well as economic modeling. For our purpose, we place more emphasis on the estimation and inference of ES and allocation statistics (marginal contribution of ES) under different situations. We also modify the back-testing rule.

Download or read book Maslowian Portfolio Theory written by Philippe De Brouwer and published by Vubpress. This book was released on 2012-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written from the perspective of a financial investor, this account supports Behavioral Portfolio Theory, draws attention to the importance of asset-liability matching, and offers a natural framework for investor-adviser dialogue and mathematical portfolio optimization. In this system, investment goals--and not investor psychology--drive investment advice; "risk" depends on the investment objective and may be different in each sub-portfolio. This comprehensive book presents an extensive overview of existing portfolio theories and behavioral finance, and introduces new theories and its practical applications.

Download or read book Fundamental Aspects of Operational Risk and Insurance Analytics written by Marcelo G. Cruz and published by John Wiley & Sons. This book was released on 2015-01-29 with total page 939 pages. Available in PDF, EPUB and Kindle. Book excerpt: A one-stop guide for the theories, applications, and statistical methodologies essential to operational risk Providing a complete overview of operational risk modeling and relevant insurance analytics, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk offers a systematic approach that covers the wide range of topics in this area. Written by a team of leading experts in the field, the handbook presents detailed coverage of the theories, applications, and models inherent in any discussion of the fundamentals of operational risk, with a primary focus on Basel II/III regulation, modeling dependence, estimation of risk models, and modeling the data elements. Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk begins with coverage on the four data elements used in operational risk framework as well as processing risk taxonomy. The book then goes further in-depth into the key topics in operational risk measurement and insurance, for example diverse methods to estimate frequency and severity models. Finally, the book ends with sections on specific topics, such as scenario analysis; multifactor modeling; and dependence modeling. A unique companion with Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk, the handbook also features: Discussions on internal loss data and key risk indicators, which are both fundamental for developing a risk-sensitive framework Guidelines for how operational risk can be inserted into a firm’s strategic decisions A model for stress tests of operational risk under the United States Comprehensive Capital Analysis and Review (CCAR) program A valuable reference for financial engineers, quantitative analysts, risk managers, and large-scale consultancy groups advising banks on their internal systems, the handbook is also useful for academics teaching postgraduate courses on the methodology of operational risk.