Stochastic Models in Life Insurance

?The book will serve as a guide to many actuarial concepts and statistical techniques in multiple decrement models and their application in calculation of premiums and reserves in life insurance produ

The book provides a sound mathematical base for life insurance mathematics and applies the underlying concepts to concrete examples. Moreover the models presented make it possible to model life insura

This 2006 book introduces and develops the basic actuarial models and underlying pricing of life-contingent pension annuities and life insurance from a unique financial perspective. The ideas and techniques are then applied to the real-world problem of generating sustainable retirement income towards the end of the human life-cycle. The role of lifetime income, longevity insurance, and systematic withdrawal plans are investigated in a parsimonious framework. The underlying technology and terminology of the book are based on continuous-time financial economics by merging analytic laws of mortality with the dynamics of equity markets and interest rates. Nonetheless, the book requires a minimal background in mathematics and emphasizes applications and examples more than proofs and theorems. It can serve as an ideal textbook for an applied course on wealth management and retirement planning in addition to being a reference for quantitatively-inclined financial planners.

Continuous-Time Models in Corporate Finance synthesizes four decades of research to show how stochastic calculus can be used in corporate finance. Combining mathematical rigor with economic intuition,

This book first provides a review of various aspects of Bayesian statistics. It then investigates three types of claims reserving models in the Bayesian framework: chain ladder models, basis expansion

"Offers a mathematical introduction to non-life insurance and, at the same time, to a multitude of applied stochastic processes. It gives detailed discussions of the fundamental models for claim sizes

The relatively young theory of structured dependence between stochastic processes has many real-life applications in areas including finance, insurance, seismology, neuroscience, and genetics. With this monograph, the first to be devoted to the modeling of structured dependence between random processes, the authors not only meet the demand for a solid theoretical account but also develop a stochastic processes counterpart of the classical copula theory that exists for finite-dimensional random variables. Presenting both the technical aspects and the applications of the theory, this is a valuable reference for researchers and practitioners in the field, as well as for graduate students in pure and applied mathematics programs. Numerous theoretical examples are included, alongside examples of both current and potential applications, aimed at helping those who need to model structured dependence between dynamic random phenomena.

Focusing on what actuaries need in practice, this introductory account provides readers with essential tools for handling complex problems and explains how simulation models can be created, used and re-used (with modifications) in related situations. The book begins by outlining the basic tools of modelling and simulation, including a discussion of the Monte Carlo method and its use. Part II deals with general insurance and Part III with life insurance and financial risk. Algorithms that can be implemented on any programming platform are spread throughout and a program library written in R is included. Numerous figures and experiments with R-code illustrate the text. The author's non-technical approach is ideal for graduate students, the only prerequisites being introductory courses in calculus and linear algebra, probability and statistics. The book will also be of value to actuaries and other analysts in the industry looking to update their skills.

Introduces the main ideas, techniques, and stochastic models of financial mathematicsFocuses on the foundations and key concepts of the modern methodology of quantitative financial analysis Explores t

The recent financial crisis has heightened the need for appropriate methodologies for managing and monitoring complex risks in financial markets. The measurement, management, and regulation of risks in portfolios composed of credits, credit derivatives, or life insurance contracts is difficult because of the nonlinearities of risk models, dependencies between individual risks, and the several thousands of contracts in large portfolios. The granularity principle was introduced in the Basel regulations for credit risk to solve these difficulties in computing capital reserves. In this book, authors Patrick Gagliardini and Christian Gouriéroux provide the first comprehensive overview of the granularity theory and illustrate its usefulness for a variety of problems related to risk analysis, statistical estimation, and derivative pricing in finance and insurance. They show how the granularity principle leads to analytical formulas for risk analysis that are simple to implement and accurate e

The recent financial crisis has heightened the need for appropriate methodologies for managing and monitoring complex risks in financial markets. The measurement, management, and regulation of risks in portfolios composed of credits, credit derivatives, or life insurance contracts is difficult because of the nonlinearities of risk models, dependencies between individual risks, and the several thousands of contracts in large portfolios. The granularity principle was introduced in the Basel regulations for credit risk to solve these difficulties in computing capital reserves. In this book, authors Patrick Gagliardini and Christian Gouriéroux provide the first comprehensive overview of the granularity theory and illustrate its usefulness for a variety of problems related to risk analysis, statistical estimation, and derivative pricing in finance and insurance. They show how the granularity principle leads to analytical formulas for risk analysis that are simple to implement and accurate e

Building on the Cambridge Element Agent Based Models of Social Life: Fundamentals (Cambridge, 2020), we move on to the next level. We do this by building agent based models of polarization and ethnocentrism. In the process, we develop: stochastic models, which add a crucial element of uncertainty to human interaction; models of human interactions structured by social networks; and 'evolutionary' models in which agents using more effective decision rules are more likely to survive and prosper than others. The aim is to leave readers with an effective toolkit for building, running and analyzing agent based modes of social interaction.

Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototy

This must-have manual provides detailed solutions to all of the 300 exercises in Dickson, Hardy and Waters' Actuarial Mathematics for Life Contingent Risks, 3 edition. This groundbreaking text on the modern mathematics of life insurance is required reading for the Society of Actuaries' (SOA) LTAM Exam. The new edition treats a wide range of newer insurance contracts such as critical illness and long-term care insurance; pension valuation material has been expanded; and two new chapters have been added on developing models from mortality data and on changing mortality. Beyond professional examinations, the textbook and solutions manual offer readers the opportunity to develop insight and understanding through guided hands-on work, and also offer practical advice for solving problems using straightforward, intuitive numerical methods. Companion Excel spreadsheets illustrating these techniques are available for free download.

This textbook provides a general overview of realistic mathematical models in life sciences, considering both deterministic and stochastic models and covering dynamical systems, game theory, stochasti

Social scientists who study religion generally believe that social networks play a central role in religious life. However, most studies draw on measures that are relatively poor proxies for capturing the effects of social networks. This book illustrates how researchers can draw on formal social network analysis methods to explore the interplay of networks and religion. The book's introductory chapters provide overviews of the social scientific study of religion and social network analysis. The remaining chapters explore a variety of topics current in the social scientific study of religion, as well as introducing a variety of social network theories and methods, such as balance theory, ego-network analysis, exponential random graph models, and stochastic actor-oriented models. By embedding social network analysis within a social scientific study of religion framework, Networks and Religion offers an array of approaches for studying the role that social networks play in religious belie

Social scientists who study religion generally believe that social networks play a central role in religious life. However, most studies draw on measures that are relatively poor proxies for capturing the effects of social networks. This book illustrates how researchers can draw on formal social network analysis methods to explore the interplay of networks and religion. The book's introductory chapters provide overviews of the social scientific study of religion and social network analysis. The remaining chapters explore a variety of topics current in the social scientific study of religion, as well as introducing a variety of social network theories and methods, such as balance theory, ego-network analysis, exponential random graph models, and stochastic actor-oriented models. By embedding social network analysis within a social scientific study of religion framework, Networks and Religion offers an array of approaches for studying the role that social networks play in religious belie

Actuaries have access to a wealth of individual data in pension and insurance portfolios, but rarely use its full potential. This book will pave the way, from methods using aggregate counts to modern developments in survival analysis. Based on the fundamental concept of the hazard rate, Part I shows how and why to build statistical models, based on data at the level of the individual persons in a pension scheme or life insurance portfolio. Extensive use is made of the R statistics package. Smooth models, including regression and spline models in one and two dimensions, are covered in depth in Part II. Finally, Part III uses multiple-state models to extend survival models beyond the simple life/death setting, and includes a brief introduction to the modern counting process approach. Practising actuaries will find this book indispensable, and students will find it helpful when preparing for their professional examinations.

The aim of this book is to promote interaction between Engineering, Finance and Insurance, as there are many models and solution methods in common for solving real-life problems in these three topics.

The theme of the book is the distribution and abundance of organisms in space and time. The core of the book lies in how local births and deaths are tied to emigration and immigration processes, and how environmental variability at different scales affects population dynamics with stochastic processes and spatial structure and shows how elementary analytical tools can be used to understand population fluctuations, synchrony, processes underlying range distributions and community structure and species coexistence. The book also shows how spatial population dynamics models can be used to understand life history evolution and aspects of evolutionary game theory. Although primarily based on analytical and numerical analyses of spatial population processes, data from several study systems are also dealt with.

The theme of the book is the distribution and abundance of organisms in space and time. The core of the book lies in how local births and deaths are tied to emigration and immigration processes, and how environmental variability at different scales affects population dynamics with stochastic processes and spatial structure and shows how elementary analytical tools can be used to understand population fluctuations, synchrony, processes underlying range distributions and community structure and species coexistence. The book also shows how spatial population dynamics models can be used to understand life history evolution and aspects of evolutionary game theory. Although primarily based on analytical and numerical analyses of spatial population processes, data from several study systems are also dealt with.

Computer simulations provide a powerful tool for understanding ecological and evolutionary systems. Simulating Ecological and Evolutionary Systems in C models a diverse range of biological processes and systems, including competition, foraging, predation, mating systems, and life-history optimization, by simulating large collections of interacting individuals. Using the widely available computer programming language C, the book starts with elementary programs modeling stochastic birth-death processes, slowly increasing programming complexity as the chapters progress. All the important features of C are covered, including arrays, files, pointers, and structures, within biologically motivated simulations. Although computer simulations of extremely complicated biological processes are released from rigid mathematical constraints, each of the simulations is also placed in the context of a mathematical formulation examined either analytically or numerically. Procedures covered include testi

These essays explore what happens when a skilful economist makes unconventional assumptions. Economic theory has traditionally relied upon a tacit and 'classical' set of assumptions that have gradually acquired a life of their own in defining how economists write and how they justify economic models. Similarly, these assumptions have acquired an autonomous character: they guide the way economists think about the world. In consequence, consideration of alternative assumptions has become taboo. These essays are substantively and stylistically novel because they break these taboos and bring new assumptions into economic theory. The papers apply this adventurous approach to a wide range of issues - from insurance markets and trade in underdeveloped countries to unemployment and discrimination. Some of the essays derive the implications for economic markets of costly asymmetric information. Others explore the findings of other social sciences such as anthropology, psychology and sociology.

As Non-Life Insurance models are strictly connected with stochastic processes, the main aim of this book is to show how classical and recent advanced stochastic models can be used to improve the stoch