Actuarial Modelling of Claim Counts

This book provides a comprehensive introduction to actuarial mathematics, covering both deterministic and stochastic models of life contingencies, as well as more advanced topics such as risk theory, credibility theory and multi-state models. This new edition includes additional material on credibility theory, continuous time multi-state models, more complex types of contingent insurances, flexible contracts such as universal life, the risk measures VaR and TVaR. Key Features: Covers much of the syllabus material on the modeling examinations of the Society of Actuaries, Canadian Institute of Actuaries and the Casualty Actuarial Society. (SOA-CIA exams MLC and C, CSA exams 3L and 4.) Extensively revised and updated with new material. Orders the topics specifically to facilitate learning. Provides a streamlined approach to actuarial notation. Employs modern computational methods. Contains a variety of exercises, both computational and theoretical, together with answers, enabling use for self-study. An ideal text for students planning for a professional career as actuaries, providing a solid preparation for the modeling examinations of the major North American actuarial associations. Furthermore, this book is highly suitable reference for those wanting a sound introduction to the subject, and for those working in insurance, annuities and pensions.

Provides a comprehensive coverage of both the deterministic and stochastic models of life contingencies, risk theory, credibility theory, multi-state models, and an introduction to modern mathematical finance. New edition restructures the material to fit into modern computational methods and provides several spreadsheet examples throughout. Covers the syllabus for the Institute of Actuaries subject CT5, Contingencies Includes new chapters covering stochastic investments returns, universal life insurance. Elements of option pricing and the Black-Scholes formula will be introduced.

The movement of sediment and associated pollutants over the landscape and into water bodies is of increasing concern with respect to pollution control, prevention of muddy floods and environmental protection. In addition, the loss of soil on site has implications for declining agricultural productivity, loss of biodiversity and decreased amenity and landscape value. The fate of sediment and the conservation of soil are important issues for land managers and decision-makers. In developing appropriate policies and solutions, managers and researchers are making greater use of erosion models to characterise the processes of erosion and their interaction with the landscape. A study of erosion requires one to think in terms of microseconds to understand the mechanics of impact of a single raindrop on a soil surface, while landscapes form over periods of thousands of years. These processes operate on scales of millimetres for single raindrops to mega-metres for continents. Erosion modelling thus covers quite a lot of ground. This book introduces the conceptual and mathematical frameworks used to formulate models of soil erosion and uses case studies to show how models are applied to a variety of purposes at a range of spatial and temporal scales. The aim is to provide land managers and others with the tools required to select a model appropriate to the type and scale of erosion problem, to show what users can expect in terms of accuracy of model predictions and to provide an appreciation of both the advantages and limitations of models. Problems covered include those arising from agriculture, the construction industry, pollution and climatic change and range in scale from farms to small and large catchments. The book will also be useful to students and research scientists as an up-to-date review of the state-of-art of erosion modelling and, through a knowledge of how models are used in practice, in highlighting the gaps in knowledge that need to be filled in order to develop even better models.

Modelling of Engineering Materials presents the background that is necessary to understand the mathematical models that govern the mechanical response of engineering materials. The book provides the basics of continuum mechanics and helps the reader to use them to understand the development of nonlinear material response of solids and fluids used in engineering applications. A brief review of simplistic and linear models used to characterize the mechanical response of materials is presented. This is followed by a description of models that characterize the nonlinear response of solids and fluids from first principles. Emphasis is given to popular models that characterize the nonlinear response of materials. The book also presents case studies of materials, where a comprehensive discussion of material characterization, experimental techniques and constitutive model development, is presented. Common principles that govern material response of both solids and fluids within a unified framework are outlined. Mechanical response in the presence of non-mechanical fields such as thermal and electrical fields applied to special materials such as shape memory materials and piezoelectric materials is also explained within the same framework.

This book is concerned with modelling the fate of organic substances in the soil. Once a chemical enters the soil it is subject to various transformation processes. It partitions between the liquid, solid and gaseous phase, it is sorbed to different binding sites with a different strength of bonding, it may decay by a simple chemical process or it may be transformed by microorganisms. Solute transport through soil and subsurface is mediated by water flow and is strongly influenced by solute sorption. To complicate matters, soil structures are heterogeneous. All these processes are embedded in a spatio-temporal hierarchy. The book brings together many different aspects of environmental fate modelling of pesticides comprising such diverse subjects as, e.g., compartment theory, nonlinear biological degradation models, modelling toxicity, parameter identification, coupling of physical and biological processes, pedotransfer functions, translation of models across scales, coupling geographical information systems with models, and FUZZY-approaches.

Understanding and predicting the behaviour of natural and human environmental systems is crucial for the effective management of the Earth’s limited resources. Recently, great advances have been made through spatial modelling. This book provides a snapshot of the latest research in modelling technologies and methodologies within five environmental fields; the cryosphere, hydrology, geomorphology, vegetation interfaces and urban environments. Spatial Modelling of the Terrestrial Environment deals with the use of remote sensing, numerical models and GIS in addressing important natural and human environmental sciences issues, focusing on the theory and application of modelling remotely sensed data within the context of environmental processes. Extensive case material exemplifies the latest research and modelling paradigms presented in the book.

Shows the newest developments in the field of multi-parametric model predictive control and optimization and their application for drug delivery systems This book is based on the Modelling, Control and Optimization of Biomedical Systems (MOBILE) project, which was created to derive intelligent computer model-based systems for optimization of biomedical drug delivery systems in the cases of diabetes, anaesthesia, and blood cancer. These systems can ensure reliable and fast calculation of the optimal drug dosage without the need for an online computer—while taking into account the specifics and constraints of the patient model, flexibility to adapt to changing patient characteristics and incorporation of the physician’s performance criteria, and maintaining the safety of the patients. Modelling Optimization and Control of Biomedical Systems covers: mathematical modelling of drug delivery systems; model analysis, parameter estimation, and approximation; optimization and control; sensitivity analysis & model reduction; multi-parametric programming and model predictive control; estimation techniques; physiologically-based patient model; control design for volatile anaesthesia; multiparametric model based approach to intravenous anaesthesia; hybrid model predictive control strategies; Type I Diabetes Mellitus; in vitro and in silico block of the integrated platform for the study of leukaemia; chemotherapy treatment as a process systems application; and more. Introduces readers to the Modelling, Control and Optimization of Biomedical Systems (MOBILE) project Presents in detail the theoretical background, computational tools, and methods that are used in all the different biomedical systems Teaches the theory for multi-parametric mixed-integer programming and explicit optimal control of volatile anaesthesia Provides an overview of the framework for modelling, optimization, and control of biomedical systems This book will appeal to students, researchers, and scientists working on the modelling, control, and optimization of biomedical systems and to those involved in cancer treatment, anaesthsia, and drug delivery systems.

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.

Understanding basin-fill evolution and the origin of stratal architectures has traditionally been based on studies of outcrops, well and seismic data, studies of and inferences on qualitative geological processes, and to a lesser extent based on quantitative observations of modern and ancient sedimentary environments. Insight gained on the basis of these studies can increasingly be tested and extended through the application of numerical and analogue forward models. Present-day stratigraphic forward modelling follows two principle lines: 1) the deterministic process-based approach, ideally with resolution of the fundamental equations of fluid and sediment motion at all scales, and 2) the stochastic approach. The process-based approach leads to improved understanding of the dynamics (physics) of the system, increasing our predictive power of how systems evolve under various forcing conditions unless the system is highly non-linear and hence difficult or perhaps even impossible to predict. The stochastic approach is more direct, relatively simple, and useful for study of more complicated or less-well understood systems. Process-based models, more than stochastic ones, are directly limited by the diversity of temporal and spatial scales and the very incomplete knowledge of how processes operate and interact on the various scales. The papers included in this book demonstrate how cross-fertilization between traditional field studies and analogue and numerical forward modelling expands our understanding of Earth-surface systems.

Learn how to use service modelling to streamline and optimize processes! Information about customer needs, the technical composition of services, and service performance are fundamental to effective service management. Service modelling is a structured approach to utilizing this information to improve the way services are delivered. Consistent application of service modelling provides the automation of processes and timely access to information. Service Modelling presents a comprehensive, up-to-date overview of the topic, presented in the context both of business processes, and of requirements stemming from the need to manage network resources. Vilho Raisanen delivers a justification for service modelling, and explains state-of-the-art concepts, frameworks and standards in detail. Service Modelling: Provides a complete and illustrated overview of state-of-the-art concepts for service modelling, covering requirements and frameworks. Includes industry initiatives, conceptual frameworks, and the work of standardisation bodies. Discusses different modelling approaches, and the positioning of modelling of services in service management and in the wider operational context. Sets the modelling framework in the context of business drivers and modelling paradigms. Illustrates principles with real-world use cases, providing both fixed Internet and mobile network examples. Relates concepts to the work of TeleManagement Forum, giving practical examples throughout. Service Modelling: Principles and Applications is an invaluable guide to service modelling for telecommunications and data communications professionals, including vendors, operators, consultants, training organizations, service and content providers, system architects and engineers for IP-based services. Educational organizations, advanced undergraduate and graduate students on telecommunications and networking courses will also find this text invaluable.