{"product_id":"loss-models-9781118343562","title":"Loss Models","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAn essential resource for constructing and analyzing advanced actuarial models\u003cbr\u003e \u003cbr\u003e \u003cbr\u003e \u003ci\u003eLoss Models: Further Topics\u003c\/i\u003e presents extended coverage of modeling through the use of tools related to risk theory, loss distributions, and survival models. The book uses these methods to construct and evaluate actuarial models in the fields of insurance and business. Providing an advanced study of actuarial methods, the book features extended discussions of risk modeling and risk measures, including Tail-Value-at-Risk. \u003ci\u003eLoss Models: Further Topics\u003c\/i\u003e contains additional material to accompany the Fourth Edition of \u003ci\u003eLoss Models: From Data to Decisions\u003c\/i\u003e, such as:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eExtreme value distributions\u003c\/li\u003e \u003cli\u003eCoxian and related distributions\u003c\/li\u003e \u003cli\u003eMixed Erlang distributions\u003c\/li\u003e \u003cli\u003eComputational and analytical methods for aggregate claim models\u003c\/li\u003e \u003cli\u003eCounting processes\u003c\/li\u003e \u003cli\u003eCompound distributions with time-dependent claim amounts\u003c\/li\u003e \u003cli\u003eCopula models\u003c\/li\u003e \u0026lt;\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Coxian and related distributions 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 3\u003c\/p\u003e \u003cp\u003e2.2 Combinations of exponentials 4\u003c\/p\u003e \u003cp\u003e2.3 Coxian-2 distributions 7\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Mixed Erlang distributions 11\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 11\u003c\/p\u003e \u003cp\u003e3.2 Members of the mixed Erlang class 12\u003c\/p\u003e \u003cp\u003e3.3 Distributional properties 18\u003c\/p\u003e \u003cp\u003e3.4 Mixed Erlang claim severity models 22\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Extreme value distributions 23\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 23\u003c\/p\u003e \u003cp\u003e4.2 Distribution of the maximum 25\u003c\/p\u003e \u003cp\u003e4.2.1 From a fixed number of losses 25\u003c\/p\u003e \u003cp\u003e4.2.2 From a random number of losses 27\u003c\/p\u003e \u003cp\u003e4.3 Stability of the maximum of the extreme value distribution 29\u003c\/p\u003e \u003cp\u003e4.4 The Fisher–Tippett theorem 30\u003c\/p\u003e \u003cp\u003e4.5 Maximum domain of attraction 32\u003c\/p\u003e \u003cp\u003e4.6 Generalized Pareto distributions 34\u003c\/p\u003e \u003cp\u003e4.7 Stability of excesses of the generalized Pareto 36\u003c\/p\u003e \u003cp\u003e4.8 Limiting distributions of excesses 37\u003c\/p\u003e \u003cp\u003e4.9 Parameter estimation 39\u003c\/p\u003e \u003cp\u003e4.9.1 Maximum likelihood estimation from the extreme value distribution 39\u003c\/p\u003e \u003cp\u003e4.9.2 Maximum likelihood estimation for the generalized Pareto distribution 42\u003c\/p\u003e \u003cp\u003e4.9.3 Estimating the Pareto shape parameter 44\u003c\/p\u003e \u003cp\u003e4.9.4 Estimating extreme probabilities 47\u003c\/p\u003e \u003cp\u003e4.9.5 Mean excess plots 49\u003c\/p\u003e \u003cp\u003e4.9.6 Further reading 49\u003c\/p\u003e \u003cp\u003e4.9.7 Exercises 49\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Analytic and related methods for aggregate claim models 51\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 51\u003c\/p\u003e \u003cp\u003e5.2 Elementary approaches 53\u003c\/p\u003e \u003cp\u003e5.3 Discrete analogues 58\u003c\/p\u003e \u003cp\u003e5.4 Right-tail asymptotics for aggregate losses 63\u003c\/p\u003e \u003cp\u003e5.4.1 Exercises 71\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Computational methods for aggregate models 73\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Recursive techniques for compound distributions 73\u003c\/p\u003e \u003cp\u003e6.2 Inversion methods 75\u003c\/p\u003e \u003cp\u003e6.2.1 Fast Fourier transform 75\u003c\/p\u003e \u003cp\u003e6.2.2 Direct numerical inversion 78\u003c\/p\u003e \u003cp\u003e6.3 Calculations with approximate distributions 80\u003c\/p\u003e \u003cp\u003e6.3.1 Arithmetic distributions 80\u003c\/p\u003e \u003cp\u003e6.3.2 Empirical distributions 83\u003c\/p\u003e \u003cp\u003e6.3.3 Piecewise linear cdf 84\u003c\/p\u003e \u003cp\u003e6.3.4 Exercises 85\u003c\/p\u003e \u003cp\u003e6.4 Comparison of methods 86\u003c\/p\u003e \u003cp\u003e6.5 The individual risk model 87\u003c\/p\u003e \u003cp\u003e6.5.1 Definition and notation 87\u003c\/p\u003e \u003cp\u003e6.5.2 Direct calculation 88\u003c\/p\u003e \u003cp\u003e6.5.3 Recursive calculation 89\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Counting Processes 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Nonhomogeneous birth processes 97\u003c\/p\u003e \u003cp\u003e7.1.1 Exercises 112\u003c\/p\u003e \u003cp\u003e7.2 Mixed Poisson processes 112\u003c\/p\u003e \u003cp\u003e7.2.1 Exercises 116\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Discrete Claim Count Models 119\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Unification of the (\u003ci\u003ea\u003c\/i\u003e, \u003ci\u003eb,\u003c\/i\u003e 1) and mixed Poisson classes 119\u003c\/p\u003e \u003cp\u003e8.2 A class of discrete generalized tail-based distributions 127\u003c\/p\u003e \u003cp\u003e8.3 Higher order generalized tail-based distributions 134\u003c\/p\u003e \u003cp\u003e8.4 Mixed Poisson properties of generalized tail-based distributions 139\u003c\/p\u003e \u003cp\u003e8.5 Compound geometric properties of generalized tail-based distributions 146\u003c\/p\u003e \u003cp\u003e8.5.1 Exercises 156\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Compound distributions with time dependent claim amounts 159\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 159\u003c\/p\u003e \u003cp\u003e9.2 A model for inflation 163\u003c\/p\u003e \u003cp\u003e9.3 A model for claim payment delays 173\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Copula models 187\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 187\u003c\/p\u003e \u003cp\u003e10.2 Sklar’s theorem and copulas 188\u003c\/p\u003e \u003cp\u003e10.3 Measures of dependency 189\u003c\/p\u003e \u003cp\u003e10.3.1 Spearman’s rho 190\u003c\/p\u003e \u003cp\u003e10.3.2 Kendall’s tau 190\u003c\/p\u003e \u003cp\u003e10.4 Tail dependence 191\u003c\/p\u003e \u003cp\u003e10.5 Archimedean copulas 192\u003c\/p\u003e \u003cp\u003e10.5.1 Exercise 197\u003c\/p\u003e \u003cp\u003e10.6 Elliptical copulas 197\u003c\/p\u003e \u003cp\u003e10.6.1 Exercise 199\u003c\/p\u003e \u003cp\u003e10.7 Extreme value copulas 200\u003c\/p\u003e \u003cp\u003e10.7.1 Exercises 202\u003c\/p\u003e \u003cp\u003e10.8 Archimax copulas 203\u003c\/p\u003e \u003cp\u003e10.9 Estimation of parameters 203\u003c\/p\u003e \u003cp\u003e10.9.1 Introduction 203\u003c\/p\u003e \u003cp\u003e10.9.2 Maximum likelihood estimation 204\u003c\/p\u003e \u003cp\u003e10.9.3 Semiparametric estimation 206\u003c\/p\u003e \u003cp\u003e10.9.4 The role of deductibles 206\u003c\/p\u003e \u003cp\u003e10.9.5 Goodness-of-fit testing 208\u003c\/p\u003e \u003cp\u003e10.9.6 An example 209\u003c\/p\u003e \u003cp\u003e10.9.7 Exercise 210\u003c\/p\u003e \u003cp\u003e10.10 Simulation from Copula Models 211\u003c\/p\u003e \u003cp\u003e10.10.1 Simulating from the Gaussian copula 213\u003c\/p\u003e \u003cp\u003e10.10.2 Simulating from the t copula 213\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Continuous-time ruin models 215\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 215\u003c\/p\u003e \u003cp\u003e11.1.1 The Poisson process 215\u003c\/p\u003e \u003cp\u003e11.1.2 The continuous-time problem 216\u003c\/p\u003e \u003cp\u003e11.2 The adjustment coefficient and Lundberg’s inequality 217\u003c\/p\u003e \u003cp\u003e11.2.1 The adjustment coefficient 217\u003c\/p\u003e \u003cp\u003e11.2.2 Lundberg’s inequality 221\u003c\/p\u003e \u003cp\u003e11.2.3 Exercises 223\u003c\/p\u003e \u003cp\u003e11.3 An integrodifferential equation 224\u003c\/p\u003e \u003cp\u003e11.3.1 Exercises 228\u003c\/p\u003e \u003cp\u003e11.4 The maximum aggregate loss 229\u003c\/p\u003e \u003cp\u003e11.4.1 Exercises 238\u003c\/p\u003e \u003cp\u003e11.5 Cramer’s asymptotic ruin formula and Tijms’ approximation 240\u003c\/p\u003e \u003cp\u003e11.5.1 Exercises 243\u003c\/p\u003e \u003cp\u003e11.6 The Brownian motion risk process 245\u003c\/p\u003e \u003cp\u003e11.7 Brownian motion and the probability of ruin 249\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Interpolation and smoothing 255\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 255\u003c\/p\u003e \u003cp\u003e12.2 Interpolation with splines 257\u003c\/p\u003e \u003cp\u003e12.2.1 Exercises 263\u003c\/p\u003e \u003cp\u003e12.3 Extrapolating with splines 264\u003c\/p\u003e \u003cp\u003e12.3.1 Exercise 265\u003c\/p\u003e \u003cp\u003e12.4 Smoothing with splines 265\u003c\/p\u003e \u003cp\u003e12.4.1 Exercise 272\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA An inventory of continuous distributions 273\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Introduction 273\u003c\/p\u003e \u003cp\u003eA.2 Transformed beta family 277\u003c\/p\u003e \u003cp\u003eA.2.1 Four-parameter distribution 277\u003c\/p\u003e \u003cp\u003eA.2.2 Three-parameter distributions 277\u003c\/p\u003e \u003cp\u003eA.2.3 Two-parameter distributions 279\u003c\/p\u003e \u003cp\u003eA.3 transformed gamma family 281\u003c\/p\u003e \u003cp\u003eA.3.1 Three-parameter distributions 281\u003c\/p\u003e \u003cp\u003eA.3.2 Two-parameter distributions 282\u003c\/p\u003e \u003cp\u003eA.3.3 One-parameter distributions 283\u003c\/p\u003e \u003cp\u003eA.4 Distributions for large losses 284\u003c\/p\u003e \u003cp\u003eA.4.1 Extreme value distributions 284\u003c\/p\u003e \u003cp\u003eA.4.2 Generalized Pareto distributions 285\u003c\/p\u003e \u003cp\u003eA.5 Other distributions 285\u003c\/p\u003e \u003cp\u003eA.6 Distributions with finite support 287\u003c\/p\u003e \u003cp\u003e\u003cb\u003eB An inventory of discrete distributions 289\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 Introduction 289\u003c\/p\u003e \u003cp\u003eB.2 The (\u003ci\u003ea\u003c\/i\u003e,\u003ci\u003e b\u003c\/i\u003e, 0) class 290\u003c\/p\u003e \u003cp\u003eB.3 The (\u003ci\u003ea\u003c\/i\u003e, \u003ci\u003eb\u003c\/i\u003e, 1) class 291\u003c\/p\u003e \u003cp\u003eB.3.1 The zero-truncated subclass 291\u003c\/p\u003e \u003cp\u003eB.3.2 The zero-modified subclass 293\u003c\/p\u003e \u003cp\u003eB.4 The compound class 294\u003c\/p\u003e \u003cp\u003eB.4.1 Some compound distributions 294\u003c\/p\u003e \u003cp\u003eB.5 A hierarchy of discrete distributions 295\u003c\/p\u003e \u003cp\u003e\u003cb\u003eC Discretization of the severity distribution 297\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eC.1 The method of rounding 297\u003c\/p\u003e \u003cp\u003eC.2 Mean preserving 298\u003c\/p\u003e \u003cp\u003eC.3 Undiscretization of a discretized distribution 298\u003c\/p\u003e \u003cp\u003e\u003cb\u003eD Solutions to Exercises 301\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eD.1 Chapter 4 301\u003c\/p\u003e \u003cp\u003eD.2 Chapter 5 303\u003c\/p\u003e \u003cp\u003eD.3 Chapter 6 304\u003c\/p\u003e \u003cp\u003eD.4 Chapter 7 305\u003c\/p\u003e \u003cp\u003eD.5 Chapter 8 312\u003c\/p\u003e \u003cp\u003eD.6 Chapter 10 316\u003c\/p\u003e \u003cp\u003eD.7 Chapter 11 319\u003c\/p\u003e \u003cp\u003eD.8 Chapter 12 333\u003c\/p\u003e \u003cp\u003eReferences 339\u003c\/p\u003e \u003cp\u003eIndex 345\u003c\/p\u003e\n\u003c\/ul\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":53515635884375,"sku":"9781118343562","price":127.76,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/loss-models-9781118343562","provider":"Book Curl","version":"1.0","type":"link"}