Download or read book Collective Risk Models with Dependence Uncertainty written by Haiyan Liu and published by . This book was released on 2017 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: We bring the recently developed framework of dependence uncertainty into collective risk models, one of the most classic models in actuarial science. We study the worst-case values of the Value-at-Risk (VaR) and the Expected Shortfall (ES) of the aggregate loss in collective risk models, under two settings of dependence uncertainty: (i) the counting random variable (claim frequency) and the individual losses (claim sizes) are independent, and the dependence of the individual losses is unknown; (ii) the dependence of the counting random variable and the individual losses is unknown. Analytical results for the worst-case values of ES are obtained. For the loss from a large portfolio of insurance policies, an asymptotic equivalence of VaR and ES is established. Our results can be used to provide approximations for VaR and ES in collective risk models with unknown dependence. Approximation errors are obtained in both cases.

Download or read book Collective Risk Models with Dependence written by Hélène Cossette and published by . This book was released on 2018 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: In actuarial science, collective risk models, in which the aggregate claim amount of a portfolio is defined in terms of random sums, play a crucial role. In these models, it is common to assume that the number of claims and their amounts are independent, even if this might not always be the case. We consider collective risk models with different dependence structures. Due to the importance of such distributions in an actuarial setting, we first investigate a collective risk model with dependence involving the family of multivariate mixed Erlang distributions. Other models based on mixtures involving bivariate and multivariate copulas in a more general setting are then presented. These different structures allow to link the number of claims to each claim amount, and to quantify the aggregate claim loss. Then, we use Archimedean and hierarchical Archimedean copulas in collective risk models, to model the dependence between the claim number random variable and the claim amount random variables involved in the random sum. Such dependence structures allow us to derive a computational methodology for the assessment of the aggregate claim amount. While being very flexible, this methodology is easy to implement, and can easily fit more complicated hierarchical structures.

Download or read book Risk Sharing and Risk Aggregation Via Risk Measures written by Haiyan Liu and published by . This book was released on 2017 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk measures have been extensively studied in actuarial science in the guise of premium calculation principles for more than 40 years, and recently, they have been the standard tool for financial institutions in both calculating regulatory capital requirement and internal risk management. This thesis focuses on two topics: risk sharing and risk aggregation via risk measures. The problem of risk sharing concerns the redistribution of a total risk among agents using risk measures to quantify risks. Risk aggregation is to study the worst-case value of aggregate risks over all possible dependence structures with given marginal risks. On the first topic, 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. We also study risk sharing in a competitive market and obtain an explicit Arrow-Debreu equilibrium. Robustness and comonotonicity of optimal allocations are investigated, and several novel advantages of ES over VaR from the perspective of a regulator are revealed. Reinsurance, as a special type of risk sharing, has been studied extensively from the perspective of either an insurer or a reinsurer. To take the interests of both parties into consideration, we study Pareto optimality of reinsurance arrangements under general model settings. We give the necessary and sufficient conditions for a reinsurance contract to be Pareto-optimal and characterize all such optimal contracts under more general model assumptions. Sufficient conditions that guarantee the existence of the Pareto-optimal contracts are obtained. When the losses of an insurer and a reinsurer are measured by the ES risk measures, we obtain the explicit forms of the Pareto-optimal reinsurance contracts under the expected value premium principle. On the second topic, we first study the aggregation of inhomogeneous risks with a special type of model uncertainty, called dependence uncertainty, in individual risk models. We establish general asymptotic equivalence results for the classes of distortion risk measures and convex risk measures under different mild conditions. The results implicitly suggest that it is only reasonable to implement a coherent risk measure for the aggregation of a large number of risks with dependence uncertainty. Then, we bring the well studied dependence uncertainty in individual risk models into collective risk models. We study the worst-case values of the VaR and the ES of the aggregate loss with identically distributed individual losses, under two settings of dependence uncertainty: (i) the counting random variable and the individual losses are independent, and the dependence of the individual losses is unknown; (ii) the dependence of the counting random variable and the individual losses is unknown. Analytical results for the worst-case values of ES are obtained. For the loss from a large portfolio of insurance policies, the asymptotic equivalence of VaR and ES is established, and approximation errors are obtained under the two dependence settings.

Download or read book On Discrete Time Risk Models with Dependence Based on Integer Valued Time Series Processes written by Jiahui Li and published by Open Dissertation Press. This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "On Discrete-time Risk Models With Dependence Based on Integer-valued Time Series Processes" by Jiahui, Li, 黎嘉慧, 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 the actuarial literature, dependence structures in risk models have been extensively studied. The main theme of this thesis is to investigate some discrete-time risk models with claim numbers modeled by integer-valued time series processes. The first model is a common shock risk model with temporal dependence between the claim numbers in each individual class of business. Specifically the Poisson MA(1) process and Poisson AR(1) process are considered for the temporal dependence. To study the ruin probability, the equations associated with the adjustment coefficients are derived. Comparisons are also made to assess the impact of the dependence structures on the ruin probability. Another model involving both the correlated classes of business and the time series approach is then studied. Thinning dependence structure is adopted to model the dependence among classes of business. The Poisson MA(1) and Poisson AR(1) processes are used to describe the claim-number processes. Adjustment coefficients and ruin probabilities are examined. Finally a discrete-time risk model with the claim number following a Poisson ARCH process is proposed. In this model, the mean of the current claim number depends on the previous observations. Within this framework, the equation for finding the adjustment coefficient is derived. Numerical studies are also carried out to examine the effect of the Poisson ARCH dependence structure on several risk measures including ruin probability, Value at Risk, and conditional tail expectation. DOI: 10.5353/th_b4852187 Subjects: Time-series analysis Risk (Insurance) - Statistical methods

Download or read book Reducing Model Risk Via Positive and Negative Dependence Assumptions written by Valeria Bignozzi and published by . This book was released on 2015 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: We give analytical bounds on the Value-at-Risk and on convex risk measures for a portfolio of random variables with fixed marginal distributions under an additional positive dependence structure. We show that assuming positive dependence information in our model leads to reduced dependence uncertainty spreads compared to the case where only marginals information is known. In more detail, we show that in our model the assumption of a positive dependence structure improves the best-possible lower estimate of a risk measure, while leaving unchanged its worst-possible upper risk bounds. In a similar way, we derive for convex risk measures that the assumption of a negative dependence structure leads to improved upper bounds for the risk while it does not help to increase the lower risk bounds in an essential way. As a result we find that additional assumptions on the dependence structure may result in essentially improved risk bounds.

Download or read book Risk Models with Dependence and Perturbation written by Zhong Li and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In ruin theory, the surplus process of an insurance company is usually modeled by the classical compound Poisson risk model or its general version, the Sparre-Andersen risk model. Under these models, the claim amounts and the inter-claim times are assumed to be independently distributed, which is not always appropriate in practice. In recent years, risk models relaxing the independence assumption have drawn increasing attention. However, previous research mostly considers the so call dependent Sparre-Andersen risk model under which the pairs of random variables consisting of the inter-claim time and the next claim amount remain independent of each other. In this thesis, we aim to examine the opposite case. Namely, the distribution of the time until the next claim depends on the size of the previous claim amount. Explicit solutions for the Gerber-Shiu function are provided for arbitrary claim sizes and various ruin-related quantities are obtained as special cases. Numerical examples are also presented. The dependent insurance risk process is further generalized to a perturbed version to incorporate small fluctuations of the underlying surplus process. Explicit solutions for the Gerber-Shiu funtion are deduced along with applications and examples. Lastly, we introduce a perturbed dependence structure into the dual risk model and study the ruin time problem. Exact solutions for the Laplace transform and the first moment of the time to ruin with an arbitrary gain-size distribution are obtained. Applications with numerical examples are provided to illustrate the impact of the dependence structure and the perturbation.

Download or read book Dependence Uncertainty Bounds and Optimization of Aggregate Risk written by Edgars Jakobsons and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Encyclopedia of Quantitative Risk Analysis and Assessment written by and published by John Wiley & Sons. This book was released on 2008-09-02 with total page 2163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading the way in this field, the Encyclopedia of Quantitative Risk Analysis and Assessment is the first publication to offer a modern, comprehensive and in-depth resource to the huge variety of disciplines involved. A truly international work, its coverage ranges across risk issues pertinent to life scientists, engineers, policy makers, healthcare professionals, the finance industry, the military and practising statisticians. Drawing on the expertise of world-renowned authors and editors in this field this title provides up-to-date material on drug safety, investment theory, public policy applications, transportation safety, public perception of risk, epidemiological risk, national defence and security, critical infrastructure, and program management. This major publication is easily accessible for all those involved in the field of risk assessment and analysis. For ease-of-use it is available in print and online.

Download or read book Model Risk Management written by Ludger Rüschendorf and published by Cambridge University Press. This book was released on 2023-12-31 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first systematic treatment of model risk, outlining the tools needed to quantify model uncertainty, to study its effects, and, in particular, to determine the best upper and lower risk bounds for various risk aggregation functionals of interest. Drawing on both numerical and analytical examples, this is a thorough reference work for actuaries, risk managers, and regulators. Supervisory authorities can use the methods discussed to challenge the models used by banks and insurers, and banks and insurers can use them to prioritize the activities on model development, identifying which ones require more attention than others. In sum, it is essential reading for all those working in portfolio theory and the theory of financial and engineering risk, as well as for practitioners in these areas. It can also be used as a textbook for graduate courses on risk bounds and model uncertainty.

Download or read book The Collective Risk Model for Aggregate Losses written by Zhi Hu and published by . This book was released on 1999 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probability The Science of Uncertainty written by Michael A. Bean and published by American Mathematical Soc.. This book was released on 2009 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the basic probability of distributions with an emphasis on applications from the areas of investments, insurance, and engineering. This book is suitable as a text for senior undergraduate and beginning graduate students in mathematics, statistics, actuarial science, finance, or engineering.

Download or read book Collective Risk Theory written by Harald Cramér and published by . This book was released on 1955 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Radiological Risk Assessment and Environmental Analysis written by John E. Till and published by Oxford University Press. This book was released on 2008-07-10 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: Radiological Risk Assessment and Environmental Analysis comprehensively explains methods used for estimating risk to people exposed to radioactive materials released to the environment by nuclear facilities or in an emergency such as a nuclear terrorist event. This is the first book that merges the diverse disciplines necessary for estimating where radioactive materials go in the environment and the risk they present to people. It is not only essential to managers and scientists, but is also a teaching text. The chapters are arranged to guide the reader through the risk assessment process, beginning with the source term (where the radioactive material comes from) and ending with the conversion to risk. In addition to presenting mathematical models used in risk assessment, data is included so the reader can perform the calculations. Each chapter also provides examples and working problems. The book will be a critical component of the rebirth of nuclear energy now taking place, as well as an essential resource to prepare for and respond to a nuclear emergency.

Download or read book Exposure of the American Population to Radioactive Fallout from Nuclear Weapons Tests written by National Research Council and published by National Academies Press. This book was released on 2003-02-25 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report is a review of the draft feasibility study that was issued at the request of Congress by the Centers for Disease Control and Prevention (CDC) and the National Cancer Institute (NCI). Over 500 atmospheric nuclear-weapons tests were conducted at various sites around the world during 1945-1980. As public awareness and concern mounted over the possible health hazards associated with exposure to the fallout from weapons testing, a feasibility study was initiated by CDC and NCI to assess the extent of the hazard. The CDC-NCI study claims that the fallout might have led to approximately 11,000 excess deaths, most caused by thyroid cancer linked to exposure to iodine-131. The committee noted that CDC and NCI used the best available data to estimate exposure and health hazards. The committee does not recommend an expanded study of exposure to radionuclides other than 131I since radiation doses from those radionuclides were much lower than those from 131I. It also recommended that CDC urge Congress to prohibit the destruction of all remaining records relevant to fallout.

Download or read book Risk Modeling for Hazards and Disasters written by Gero Michel and published by Elsevier. This book was released on 2017-08-29 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk Modeling for Hazards and Disasters covers all major aspects of catastrophe risk modeling, from hazards through to financial analysis. It explores relevant new science in risk modeling, indirect losses, assessment of impact and consequences to insurance losses, and current changes in risk modeling practice, along with case studies. It also provides further insight into the shortcomings of current models and examines model risk and ideas to diversify risk assessment. Risk Modeling for Hazards and Disasters instructs readers on how to assess, price and then hedge the losses from natural and manmade catastrophes. This book reviews current model development and science and explains recent changes in the catastrophe modeling space, including new initiatives covering uncertainty and big data in the assessment of risk for insurance pricing and portfolio management. Edited by a leading expert in both hazards and risk, this book is authored by a global panel including major modeling vendors, modeling consulting firms, and well-known catastrophe modeling scientists. Risk Modeling for Hazards and Disasters provides important insight into how models are used to price and manage risk. Includes high profile case studies such as the Newcastle earthquake, Hurricane Andrew and Hurricane Katrina Provides crucial information on new ideas and platforms that will help address the new demands for risk management and catastrophe risk reporting Presents the theory and practice needed to know how models are created and what is and what is not important in the modeling process Covers relevant new science in risk modeling, indirect losses, assessment of impact and consequences to insurance losses, and current changes in risk modeling practice, along with case studies

Download or read book Applied Stochastic Models and Control for Finance and Insurance written by Charles S. Tapiero and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Stochastic Models and Control for Finance and Insurance presents at an introductory level some essential stochastic models applied in economics, finance and insurance. Markov chains, random walks, stochastic differential equations and other stochastic processes are used throughout the book and systematically applied to economic and financial applications. In addition, a dynamic programming framework is used to deal with some basic optimization problems. The book begins by introducing problems of economics, finance and insurance which involve time, uncertainty and risk. A number of cases are treated in detail, spanning risk management, volatility, memory, the time structure of preferences, interest rates and yields, etc. The second and third chapters provide an introduction to stochastic models and their application. Stochastic differential equations and stochastic calculus are presented in an intuitive manner, and numerous applications and exercises are used to facilitate their understanding and their use in Chapter 3. A number of other processes which are increasingly used in finance and insurance are introduced in Chapter 4. In the fifth chapter, ARCH and GARCH models are presented and their application to modeling volatility is emphasized. An outline of decision-making procedures is presented in Chapter 6. Furthermore, we also introduce the essentials of stochastic dynamic programming and control, and provide first steps for the student who seeks to apply these techniques. Finally, in Chapter 7, numerical techniques and approximations to stochastic processes are examined. This book can be used in business, economics, financial engineering and decision sciences schools for second year Master's students, as well as in a number of courses widely given in departments of statistics, systems and decision sciences.

Download or read book Collective and Mixed Risk Models written by Liansheng Chen and published by . This book was released on 1995 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: