Download or read book Applications of Comonotonicity in Risk Sharing and Optimal Allocation written by Yian Rong and published by . This book was released on 2017-01-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Applications of Comonotonicity in Risk-sharing and Optimal Allocation" by Yian, Rong, 戎軼安, 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: Over the past decades, researchers in economics, financial mathematics and actuarial science have introduced results to the concept of comonotonicity in their respective fields of interest. Comonotonicity is a very strong dependence structure and is very often mistaken as a dependence structure that is too extreme and unrealistic. However, the concept of comonotonicity is actually a useful tool for solving several research and practical problems in capital allocation, risk sharing and optimal allocation. The first topic of this thesis is focused on the application of comonotonicity in optimal capital allocation. The Enterprise Risk Management process of a financial institution usually contains a procedure to allocate the total risk capital of the company into its different business units. Dhaene et al. (2012) proposed a unifying capital allocation framework by considering some general deviation measures. This general framework is extended to a more general optimization problem of minimizing separable convex function with a linear constraint and box constraints. A new approach of solving this constrained minimization problem explicitly by the concept of comonotonicity is developed. Instead of the traditional Kuhn-Tucker theory, a method of expressing each convex function as the expected stop-loss of some suitable random variable is used to solve the optimization problem. Then, some results in convex analysis with infimum-convolution are derived using the result of this new approach. Next, Borch's theorem is revisited from the perspective of comonotonicity. The optimal solution to the Pareto optimal risk-sharing problem can be obtained by the Lagrangian method or variational arguments. Here, I propose a new method, which is based on a Breeden-Litzanbeger type integral representation formula for increasing convex functions. It enables the transform of the objective function into a sum of mixtures of stop-losses. Necessary conditions for the existence of optimal solution are then discussed. The explicit solution obtained allows us to show that the risk-sharing problem is indeed a "point-wise" problem, and hence the value function can be obtained immediately using the notion of supremum-convolution in convex analysis. In addition to the above classical risk-sharing and capital allocation problems, the problem of minimizing a separable convex objective subject to an ordering restriction is then studied. Best et al. (2000) proposed a pool adjacent violators algorithm to compute the optimal solution. Instead, we show that using the concept of comonotonicity and the technique of dynamic programming the solution can be derived in a recursive manner. By identifying the right-hand derivative of the convex functions with distribution functions of some suitable random variables, we rewrite the objective function into a sum of expected deviations. This transformation and the fact that the expected deviation is a convex function enable us to solve the minimizing problem. DOI: 10.5353/th_b5334876 Subjects: Investments - Mathematical models Risk management - Mathematical models

Download or read book Applications of Comonotonicity in Risk sharing and Optimal Allocation written by 戎軼安 and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Comonotonicity and Pareto Optimality with Application to Collaborative Insurance written by M. Denuit and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two by-now folkloric results in the theory of risk sharing are that (i) any feasible allocation is convex-order-dominated by a comonotonic allocation; and (ii) an allocation is Pareto optimal for the convex order if and only if it is comonotonic. Here, comonotonicity corresponds to the no-sabotage condition, which aligns the interests of all parties involved. Several proofs of these two results have been provided in the literature, mostly based on the comonotonic improvement algorithm of Landsberger and Meilijson (1994) and a limit argument based on the Martingale Convergence Theorem. However, no proof of (i) is explicit enough to allow for an easy algorithmic implementation in practice; and no proof of (ii) provides a closed-form characterization of Pareto optima. In this paper, we provide novel proofs of these foundational results. Our proof of (i) is based on the theory of majorization and an extension of a result of Lorentz and Shimogaki (1968), which allows us to provide an explicit algorithmic construction that can be easily implemented. In addition, our proof of (ii) leads to a crisp closed-form characterization of Pareto-optimal allocations in terms of alpha-quantiles (mixed quantiles). An application to collaborative insurance, or decentralized risk sharing, illustrates the relevance of these results.

Download or read book Advanced Mathematical Methods for Finance written by Julia Di Nunno and published by Springer Science & Business Media. This book was released on 2011-03-29 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced at various levels. The chosen blend of topics gives an overview of the frontiers of mathematics for finance. New results, new methods and new models are all introduced in different forms according to the subject. Additionally, the existing literature on the topic is reviewed. The diversity of the topics makes the book suitable for graduate students, researchers and practitioners in the areas of financial modeling and quantitative finance. The chapters will also be of interest to experts in the financial market interested in new methods and products. This volume presents the results of the European ESF research networking program Advanced Mathematical Methods for Finance.

Download or read book Modern Actuarial Risk Theory written by Rob Kaas and published by Springer Science & Business Media. This book was released on 2008-12-03 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern Actuarial Risk Theory contains what every actuary needs to know about non-life insurance mathematics. It starts with the standard material like utility theory, individual and collective model and basic ruin theory. Other topics are risk measures and premium principles, bonus-malus systems, ordering of risks and credibility theory. It also contains some chapters about Generalized Linear Models, applied to rating and IBNR problems. As to the level of the mathematics, the book would fit in a bachelors or masters program in quantitative economics or mathematical statistics. This second and.

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 Decentralized Insurance written by Runhuan Feng and published by Springer Nature. This book was released on 2023-05-21 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book offers an introduction to the technical foundation of decentralized insurance models, for advanced undergraduate students, graduate students and practitioners. The book is self-contained and anyone with a basic knowledge of probability and statistics should be able to follow through the entire book. It adopts a minimalist approach to describe the essential elements and first principles so that readers can get a gist of these models without being overwhelmed with too much technicality. It can be used as a reference for business model designs. The inclusion of exercises and practical examples makes the book suitable for advanced courses on decentralized insurance and risk sharing. There is a mix of industry practices and academic models presented in this book. The exposition starts with an overview of historic and current business practices and preliminaries on the mathematics and economics of risk and insurance. A bird's-eye view of traditional insurance is provided as a benchmark for various topics to be used in contrast with decentralized insurance. The book then continues with decentralized insurance practices around the world, including online mutual aid originated in China, takaful from the Islamic world, peer-to-peer insurance in the West, catastrophe risk pooling for Carribean countries, etc. Theories of aggregate risk pooling and peer-to-peer risk exchanges are provided for readers to appreciate the mathematical foundation of risk sharing. A unified framework of decentralized insurance is presented to show a structured approach to the economic design of decentralized business models. The book ends with a technical review of blockchain and decentralized finance (DeFi) insurance applications.

Download or read book Risk Sharing for Individual Risks written by Hirbod Assa and published by . This book was released on 2014 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by reinsurance applications, we consider an optimal risk sharing problem for individual risks. In a framework where the market participants' preferences are according to the sub-additive and law-invariant risk measures, first we characterize the optimal individual risk sharing allocations. Then, we introduce a Choquet risk measure, associated with a given law-invariant coherent risk measure and, by using that, we characterize the optimal risk sharing allocations for the individual risks.

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.

Download or read book Dependence Modeling written by Harry Joe and published by World Scientific. This book was released on 2011 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Introduction : Dependence modeling / D. Kurowicka -- 2. Multivariate copulae / M. Fischer -- 3. Vines arise / R.M. Cooke, H. Joe and K. Aas -- 4. Sampling count variables with specified Pearson correlation : A comparison between a naive and a C-vine sampling approach / V. Erhardt and C. Czado -- 5. Micro correlations and tail dependence / R.M. Cooke, C. Kousky and H. Joe -- 6. The Copula information criterion and Its implications for the maximum pseudo-likelihood estimator / S. Gronneberg -- 7. Dependence comparisons of vine copulae with four or more variables / H. Joe -- 8. Tail dependence in vine copulae / H. Joe -- 9. Counting vines / O. Morales-Napoles -- 10. Regular vines : Generation algorithm and number of equivalence classes / H. Joe, R.M. Cooke and D. Kurowicka -- 11. Optimal truncation of vines / D. Kurowicka -- 12. Bayesian inference for D-vines : Estimation and model selection / C. Czado and A. Min -- 13. Analysis of Australian electricity loads using joint Bayesian inference of D-vines with autoregressive margins / C. Czado, F. Gartner and A. Min -- 14. Non-parametric Bayesian belief nets versus vines / A. Hanea -- 15. Modeling dependence between financial returns using pair-copula constructions / K. Aas and D. Berg -- 16. Dynamic D-vine model / A. Heinen and A. Valdesogo -- 17. Summary and future directions / D. Kurowicka

Download or read book Journal of Mathematical Economics written by and published by . This book was released on 2000 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Selected Works of E L Lehmann written by Javier Rojo and published by Springer Science & Business Media. This book was released on 2012-01-14 with total page 1104 pages. Available in PDF, EPUB and Kindle. Book excerpt: These volumes present a selection of Erich L. Lehmann’s monumental contributions to Statistics. These works are multifaceted. His early work included fundamental contributions to hypothesis testing, theory of point estimation, and more generally to decision theory. His work in Nonparametric Statistics was groundbreaking. His fundamental contributions in this area include results that came to assuage the anxiety of statisticians that were skeptical of nonparametric methodologies, and his work on concepts of dependence has created a large literature. The two volumes are divided into chapters of related works. Invited contributors have critiqued the papers in each chapter, and the reprinted group of papers follows each commentary. A complete bibliography that contains links to recorded talks by Erich Lehmann – and which are freely accessible to the public – and a list of Ph.D. students are also included. These volumes belong in every statistician’s personal collection and are a required holding for any institutional library.

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.

Download or read book Three Essays on the Optimal Allocation of Risk with Illiquidity Intergenerational Sharing and Systemic Institutions written by Daniel Dimitrov and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Information Incentives and Effects of Risk Sharing on the Real Economy written by Mark H. Liu and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the absence of market imperfections, the mutuality principle leads to efficient risk sharing and the Pareto optimal asset allocations. With market imperfections such as transaction costs and information asymmetry, risk-sharing becomes costly, and it can even lead to financial crises. We emphasize the impact of risk-sharing on the real economy, especially the incentives for the insured party to take on excessive risks because the downsides are borne by the insurer (i.e., the moral hazard problem). We then review selective literature and summarize papers included in this issue, grouping them into three broad categories: risk identification, risk measurement, and risk management techniques. We conclude by outlining several streams of future research, including mechanisms to monitor excessive risk-taking, how to mitigate risk interconnectedness, and the potential applications of FinTech in risk sharing.

Download or read book Practical Methods of Financial Engineering and Risk Management written by Rupak Chatterjee and published by Apress. This book was released on 2014-09-26 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk control, capital allocation, and realistic derivative pricing and hedging are critical concerns for major financial institutions and individual traders alike. Events from the collapse of Lehman Brothers to the Greek sovereign debt crisis demonstrate the urgent and abiding need for statistical tools adequate to measure and anticipate the amplitude of potential swings in the financial markets—from ordinary stock price and interest rate moves, to defaults, to those increasingly frequent "rare events" fashionably called black swan events. Yet many on Wall Street continue to rely on standard models based on artificially simplified assumptions that can lead to systematic (and sometimes catastrophic) underestimation of real risks. In Practical Methods of Financial Engineering and Risk Management, Dr. Rupak Chatterjee— former director of the multi-asset quantitative research group at Citi—introduces finance professionals and advanced students to the latest concepts, tools, valuation techniques, and analytic measures being deployed by the more discerning and responsive Wall Street practitioners, on all operational scales from day trading to institutional strategy, to model and analyze more faithfully the real behavior and risk exposure of financial markets in the cold light of the post-2008 realities. Until one masters this modern skill set, one cannot allocate risk capital properly, price and hedge derivative securities realistically, or risk-manage positions from the multiple perspectives of market risk, credit risk, counterparty risk, and systemic risk. The book assumes a working knowledge of calculus, statistics, and Excel, but it teaches techniques from statistical analysis, probability, and stochastic processes sufficient to enable the reader to calibrate probability distributions and create the simulations that are used on Wall Street to valuate various financial instruments correctly, model the risk dimensions of trading strategies, and perform the numerically intensive analysis of risk measures required by various regulatory agencies.

Download or read book Economics and Finance of Risk and of the Future written by Robert Kast and published by John Wiley & Sons. This book was released on 2006-06-14 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses real-world examples to show how individual and collective risks can be blended and treated in a reliable decision-making framework that draws its inspiration from decision theory and market based mechanisms. It then goes into deeper detail by looking at the implications of having to face risks (a) where some kind of probabilistic description is available and (b) where none is available, using the example of insurable risks vs non-insurable risks. Again, by using real-world examples it shows how decision-makers can cope with such situations by a proper understanding and use of modern financial techniques.