Author: Fangda Liu
Publisher:
ISBN:
Category :
Languages : en
Pages : 25
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Book Description
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.
Author: Ludger Rüschendorf
Publisher: Springer Science & Business Media
ISBN: 364233590X
Category : Mathematics
Languages : en
Pages : 414
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Book Description
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.
Author: Tomer Shushi
Publisher:
ISBN:
Category :
Languages : en
Pages : 110
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Book Description
Author: Hansjörg Albrecher
Publisher: John Wiley & Sons
ISBN: 0470772689
Category : Mathematics
Languages : en
Pages : 366
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Book Description
Reinsurance: Actuarial and Statistical Aspects provides a survey of both the academic literature in the field as well as challenges appearing in reinsurance practice and puts the two in perspective. The book is written for researchers with an interest in reinsurance problems, for graduate students with a basic knowledge of probability and statistics as well as for reinsurance practitioners. The focus of the book is on modelling together with the statistical challenges that go along with it. The discussed statistical approaches are illustrated alongside six case studies of insurance loss data sets, ranging from MTPL over fire to storm and flood loss data. Some of the presented material also contains new results that have not yet been published in the research literature. An extensive bibliography provides readers with links for further study.
Author: Bruno Spilak
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Englische Version: This dissertation shows the potential of machine learning methods for managing tail risk in a non-stationary and high-dimensional setting. For this, we compare in a robust manner data-dependent approaches from parametric or non-parametric statistics with data-adaptive methods. As these methods need to be reproducible to ensure trust and transparency, we start by proposing a new platform called Quantinar, which aims to set a new standard for academic publications. In the second chapter, we dive into the core subject of this thesis which compares various parametric, local parametric, and non-parametric methods to create a dynamic trading strategy that protects against tail risk in Bitcoin cryptocurrency. In the third chapter, we propose a new portfolio allocation method, called NMFRB, that deals with high dimensions thanks to a dimension reduction technique, convex Non-negative Matrix Factorization. This technique allows us to find latent interpretable portfolios that are diversified out-of-sample. We show in two universes that the proposed method outperforms other classical machine learning-based methods such as Hierarchical Risk Parity (HRP) concerning risk-adjusted returns. We also test the robustness of our results via Monte Carlo simulation. Finally, the last chapter combines our previous approaches to develop a tail-risk protection strategy for portfolios: we extend the NMFRB to tail-risk measures, we address the non-linear relationships between assets during tail events by developing a specific non-linear latent factor model, finally, we develop a dynamic tail risk protection strategy that deals with the non-stationarity of asset returns using classical econometrics models. We show that our strategy is successful at reducing large drawdowns and outperforms other modern tail-risk protection strategies such as the Value-at-Risk-spread strategy. We verify our findings by performing various data snooping tests.
Author: Marta Mylyan
Publisher:
ISBN:
Category :
Languages : en
Pages : 110
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Book Description
Author: Harry Joe
Publisher: World Scientific
ISBN: 981429988X
Category : Business & Economics
Languages : en
Pages : 370
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Book Description
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
Author: Stephen P. Boyd
Publisher: Cambridge University Press
ISBN: 9780521833783
Category : Business & Economics
Languages : en
Pages : 744
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Book Description
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Author: Klaus Sandmann
Publisher: Springer Science & Business Media
ISBN: 366204790X
Category : Business & Economics
Languages : en
Pages : 325
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Book Description
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.
Author: Michel Denuit
Publisher: John Wiley & Sons
ISBN: 0470016442
Category : Business & Economics
Languages : en
Pages : 458
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Book Description
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.
