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Optimal Risk Transfer Under Quantile Based Risk Measures
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Book Synopsis Optimal Risk Transfer Under Quantile-Based Risk Measures by : Alexandru Vali Asimit
Download or read book Optimal Risk Transfer Under Quantile-Based Risk Measures written by Alexandru Vali Asimit and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical problem of identifying the optimal reinsurance arrangement for a one-period model is examined under some risk measure criteria. We develop a new methodology via a two-stage optimisation procedure which allows us to not only recover some existing results in the literature, but also makes possible the analysis of high dimensional problems in which the insurance company diversifies its risk with multiple reinsurance counter-parties, where the insurer risk position and the premium charged by the reinsurers are risk quantile functions. Closed form solutions are elaborated for some particular settings, although numerical methods for the second part of our procedure represent viable alternatives for the ease of implementing it in more complex scenarios. Furthermore, we discuss some approaches to obtain more robust results.
Book Synopsis Quantile-Based Risk Sharing by : Paul Embrechts
Download or read book Quantile-Based Risk Sharing written by Paul Embrechts and published by . This book was released on 2017 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: We address the problem of risk sharing among agents using a two-parameter class of quantile-based risk measures, the so-called Range-Value-at-Risk (RVaR), as their preferences. The family of RVaR includes the Value-at-Risk (VaR) and the Expected Shortfall (ES), the two popular and competing regulatory risk measures, as special cases. We first establish an inequality for RVaR-based risk aggregation, showing that RVaR satisfies a special form of subadditivity. Then, the Pareto-optimal risk sharing problem is solved through explicit construction. To study risk sharing in a competitive market, an Arrow-Debreu equilibrium is established for some simple, yet natural settings. Further, we investigate the problem of model uncertainty in risk sharing, and show that, generally, a robust optimal allocation exists if and only if none of the underlying risk measures is a VaR. Practical implications of our main results for risk management and policy makers are discussed, and several novel advantages of ES over VaR from the perspective of a regulator are thereby revealed.
Book Synopsis Risk Management in Turbulent Times by : Gilles Beneplanc
Download or read book Risk Management in Turbulent Times written by Gilles Beneplanc and published by OUP USA. This book was released on 2011-08-05 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The risk management models used by banks and insurance companies are designed for when financial markets behave smoothly and efficiently. However, large risks materialize very often, and financial markets periodically go through bubbles and crashes. This book provides a road map of the most popular models of risk management and shows how they can be adapted to "turbulent times."
Book Synopsis Inf-convolution and Optimal Allocations for Tail Risk Measures by : Fangda Liu
Download or read book Inf-convolution and Optimal Allocations for Tail Risk Measures written by Fangda Liu and published by . This book was released on 2019 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inspired by the recent developments in risk sharing problems for the Value-at-Risk (VaR), the Expected Shortfall (ES), or the Range-Value-at-Risk (RVaR), we study the optimization of risk sharing for general tail risk measures. Explicit formulas of the inf-convolution and Pareto optimal allocations are obtained in the case of a mixed collection of left and right VaRs, and in that of a VaR and another tail risk measure. The inf-convolution of tail risk measures is shown to be a tail risk measure with an aggregated tail parameter, a phenomenon very similar to the cases of VaR , ES and RVaR. The technical conclusions are quite general without assuming any form of convexity of the tail risk measures. Moreover, we find, via several results, that the roles of left and right VaRs are generally asymmetric in the optimization problems. Our analysis generalizes in several directions the recent work on quantile-based risk sharing.
Book Synopsis Pricing Insurance Risk by : Stephen J. Mildenhall
Download or read book Pricing Insurance Risk written by Stephen J. Mildenhall and published by John Wiley & Sons. This book was released on 2022-06-15 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: PRICING INSURANCE RISK A comprehensive framework for measuring, valuing, and managing risk Pricing Insurance Risk: Theory and Practice delivers an accessible and authoritative account of how to determine the premium for a portfolio of non-hedgeable insurance risks and how to allocate it fairly to each portfolio component. The authors synthesize hundreds of academic research papers, bringing to light little-appreciated answers to fundamental questions about the relationships between insurance risk, capital, and premium. They lean on their industry experience throughout to connect the theory to real-world practice, such as assessing the performance of business units, evaluating risk transfer options, and optimizing portfolio mix. Readers will discover: Definitions, classifications, and specifications of risk An in-depth treatment of classical risk measures and premium calculation principles Properties of risk measures and their visualization A logical framework for spectral and coherent risk measures How risk measures for capital and pricing are distinct but interact Why the cost of capital, not capital itself, should be allocated The natural allocation method and how it unifies marginal and risk-adjusted probability approaches Applications to reserve risk, reinsurance, asset risk, franchise value, and portfolio optimization Perfect for actuaries working in the non-life or general insurance and reinsurance sectors, Pricing Insurance Risk: Theory and Practice is also an indispensable resource for banking and finance professionals, as well as risk management professionals seeking insight into measuring the value of their efforts to mitigate, transfer, or bear nonsystematic risk.
Book Synopsis Mathematical Risk Analysis by : Ludger Rüschendorf
Download or read book Mathematical Risk Analysis written by Ludger Rüschendorf and published by Springer Science & Business Media. This book was released on 2013-03-12 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author's particular interest in the area of risk measures is to combine this theory with the analysis of dependence properties. The present volume gives an introduction of basic concepts and methods in mathematical risk analysis, in particular of those parts of risk theory that are of special relevance to finance and insurance. Describing the influence of dependence in multivariate stochastic models on risk vectors is the main focus of the text that presents main ideas and methods as well as their relevance to practical applications. The first part introduces basic probabilistic tools and methods of distributional analysis, and describes their use to the modeling of dependence and to the derivation of risk bounds in these models. In the second, part risk measures with a particular focus on those in the financial and insurance context are presented. The final parts are then devoted to applications relevant to optimal risk allocation, optimal portfolio problems as well as to the optimization of insurance contracts. Good knowledge of basic probability and statistics as well as of basic general mathematics is a prerequisite for comfortably reading and working with the present volume, which is intended for graduate students, practitioners and researchers and can serve as a reference resource for the main concepts and techniques.
Download or read book After VaR written by Kevin Dowd and published by . This book was released on 2006 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Portfolio Optimization and Performance Analysis by : Jean-Luc Prigent
Download or read book Portfolio Optimization and Performance Analysis written by Jean-Luc Prigent and published by CRC Press. This book was released on 2007-05-07 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: In answer to the intense development of new financial products and the increasing complexity of portfolio management theory, Portfolio Optimization and Performance Analysis offers a solid grounding in modern portfolio theory. The book presents both standard and novel results on the axiomatics of the individual choice in an uncertain framework, cont
Book Synopsis Actuarial Theory for Dependent Risks by : Michel Denuit
Download or read book Actuarial Theory for Dependent Risks written by Michel Denuit and published by John Wiley & Sons. This book was released on 2006-05-01 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The increasing complexity of insurance and reinsurance products has seen a growing interest amongst actuaries in the modelling of dependent risks. For efficient risk management, actuaries need to be able to answer fundamental questions such as: Is the correlation structure dangerous? And, if yes, to what extent? Therefore tools to quantify, compare, and model the strength of dependence between different risks are vital. Combining coverage of stochastic order and risk measure theories with the basics of risk management and stochastic dependence, this book provides an essential guide to managing modern financial risk. * Describes how to model risks in incomplete markets, emphasising insurance risks. * Explains how to measure and compare the danger of risks, model their interactions, and measure the strength of their association. * Examines the type of dependence induced by GLM-based credibility models, the bounds on functions of dependent risks, and probabilistic distances between actuarial models. * Detailed presentation of risk measures, stochastic orderings, copula models, dependence concepts and dependence orderings. * Includes numerous exercises allowing a cementing of the concepts by all levels of readers. * Solutions to tasks as well as further examples and exercises can be found on a supporting website. An invaluable reference for both academics and practitioners alike, Actuarial Theory for Dependent Risks will appeal to all those eager to master the up-to-date modelling tools for dependent risks. The inclusion of exercises and practical examples makes the book suitable for advanced courses on risk management in incomplete markets. Traders looking for practical advice on insurance markets will also find much of interest.
Book Synopsis Optimal Risk Sharing for Law Invariant Monetary Utility Functions by : Elyes Jouini
Download or read book Optimal Risk Sharing for Law Invariant Monetary Utility Functions written by Elyes Jouini and published by . This book was released on 2007 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the problem of optimal risk sharing of some given total risk between two economic agents characterized by law-invariant monetary utility functions or equivalently, law-invariant risk measures. We first prove existence of an optimal risk sharing allocation which is in addition increasing in terms of the total risk. We next provide an explicit characterization in the case where both agents' utility functions are comonotone. The general form of the optimal contracts turns out to be given by a sum of options (stop-loss contracts, in the language of insurance) on the total risk. In order to show the robustness of this type of contracts to more general utility functions, we introduce a new notion of strict risk aversion conditionally on lower tail events, which is typically satisfied by the semi-deviation and the entropic risk measures. Then, in the context of an AV@R-agent facing an agent with strict monotone preferences and exhibiting strict risk aversion conditional on lower tail events, we prove that optimal contracts again are European options on the total risk.
Book Synopsis Risk-Averse Optimization and Control by : Darinka Dentcheva
Download or read book Risk-Averse Optimization and Control written by Darinka Dentcheva and published by Springer Nature. This book was released on with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Under and Overestimation of Risk and Other Problems with Risk Measures by : Fernando Hideki Kato
Download or read book The Under and Overestimation of Risk and Other Problems with Risk Measures written by Fernando Hideki Kato and published by . This book was released on 2006 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some problems with risk measures will be shown in this paper. In particular, quantile-based risk measures, such as VaR and CVaR, cause either under or overestimation of risk for general distributions. This is an undesired problem from the point of view of a rational investor. A better risk measure is the Downside Risk.
Book Synopsis Stochastic Finance by : Hans Föllmer
Download or read book Stochastic Finance written by Hans Föllmer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-07-25 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This fourth, newly revised edition contains more than one hundred exercises. It also includes material on risk measures and the related issue of model uncertainty, in particular a chapter on dynamic risk measures and sections on robust utility maximization and on efficient hedging with convex risk measures. Contents: Part I: Mathematical finance in one period Arbitrage theory Preferences Optimality and equilibrium Monetary measures of risk Part II: Dynamic hedging Dynamic arbitrage theory American contingent claims Superhedging Efficient hedging Hedging under constraints Minimizing the hedging error Dynamic risk measures
Book Synopsis A Guided Tour of Artificial Intelligence Research by : Pierre Marquis
Download or read book A Guided Tour of Artificial Intelligence Research written by Pierre Marquis and published by Springer Nature. This book was released on 2020-05-08 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide an overview of AI research, ranging from basic work to interfaces and applications, with as much emphasis on results as on current issues. It is aimed at an audience of master students and Ph.D. students, and can be of interest as well for researchers and engineers who want to know more about AI. The book is split into three volumes: - the first volume brings together twenty-three chapters dealing with the foundations of knowledge representation and the formalization of reasoning and learning (Volume 1. Knowledge representation, reasoning and learning) - the second volume offers a view of AI, in fourteen chapters, from the side of the algorithms (Volume 2. AI Algorithms) - the third volume, composed of sixteen chapters, describes the main interfaces and applications of AI (Volume 3. Interfaces and applications of AI). Implementing reasoning or decision making processes requires an appropriate representation of the pieces of information to be exploited. This first volume starts with a historical chapter sketching the slow emergence of building blocks of AI along centuries. Then the volume provides an organized overview of different logical, numerical, or graphical representation formalisms able to handle incomplete information, rules having exceptions, probabilistic and possibilistic uncertainty (and beyond), as well as taxonomies, time, space, preferences, norms, causality, and even trust and emotions among agents. Different types of reasoning, beyond classical deduction, are surveyed including nonmonotonic reasoning, belief revision, updating, information fusion, reasoning based on similarity (case-based, interpolative, or analogical), as well as reasoning about actions, reasoning about ontologies (description logics), argumentation, and negotiation or persuasion between agents. Three chapters deal with decision making, be it multiple criteria, collective, or under uncertainty. Two chapters cover statistical computational learning and reinforcement learning (other machine learning topics are covered in Volume 2). Chapters on diagnosis and supervision, validation and explanation, and knowledge base acquisition complete the volume.
Book Synopsis Risk Quantification and Allocation Methods for Practitioners by : Montserrat Guillén
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.
Book Synopsis Optimal Numeraires for Risk Measures by : Damir Filipović
Download or read book Optimal Numeraires for Risk Measures written by Damir Filipović and published by . This book was released on 2007 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operational Risk written by Andreas Jobst and published by International Monetary Fund. This book was released on 2007-10-01 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates the generalized parametric measurement methods of aggregate operational risk in compliance with the regulatory capital standards for operational risk in the New Basel Capital Accord ("Basel II"). Operational risk is commonly defined as the risk of loss resulting from inadequate or failed internal processes and information systems, from misconduct by people or from unforeseen external events. Our analysis informs an integrated assessment of the quantification of operational risk exposure and the consistency of current capital rules on operational risk based on generalized parametric estimation.
