Books

Actuarial Foundations for Life and Health Insurance: Modeling, Pricing and Reserving is the English-language version of our book Actuariat des assurances de personnes : modélisation, tarification et provisionnement, originally published in French by Economica and now out of print.

The book develops a unified mathematical framework for the modelling, pricing and reserving of life and health insurance contracts. Its central idea is to represent the evolution of an insured individual through continuous-time finite-state stochastic processes, making it possible to treat a wide range of products within a common actuarial framework.

Starting from classical life insurance, the book progressively introduces multiple-decrement and multiple-life models, before turning to more general Markov and semi-Markov models for risks such as hospitalization, disability, long-term care and unemployment. Particular attention is paid to the statistical estimation of transition intensities, so that probabilistic modelling remains closely connected to observable insurance data. The final part considers further actuarial applications, including policy surrenders, surplus distribution and the valuation of life insurance contracts.

The presentation deliberately combines probability, statistics and actuarial practice. Mathematical models are introduced progressively, together with the corresponding pricing formulas, reserve calculations and statistical estimation methods. The book is intended for actuarial students, practising actuaries and researchers interested in the probabilistic foundations of life and health insurance.

Risk Exchanges: Foundations, Models, and Actuarial Applications is a monograph currently under preparation with Michel Denuit. The book aims to provide a unified actuarial framework for understanding how risks can be retained, transferred, pooled, redistributed, or compensated across agents and institutions.

Rather than starting from a particular insurance product or business model, the book begins with the structure of the risk exchange itself. A common two-date framework is used to connect classical insurance, optimal risk allocation, mutualization, peer-to-peer arrangements, fully funded schemes, and hybrid mechanisms combining internal risk sharing with external protection. Particular attention is paid to actuarial fairness, individual rationality, Pareto efficiency, stochastic orders, and the information required to implement different sharing rules.

The book then develops several families of risk-sharing mechanisms in greater depth, including linear risk sharing and conditional mean risk sharing (CMRS). It studies their probabilistic structure, diversification properties, tail behaviour, computation, and dynamic extensions. A substantial part of the book is devoted to large-pool asymptotics, with laws of large numbers, central limit results, heavy-tailed limits, and large-deviation methods used to understand how risk-sharing mechanisms behave as the number of participants increases.

The final part turns to actuarial applications, including cost-of-capital pricing, collaborative insurance with reinsurance protection, mutual-aid platforms, parametric insurance with residual basis-risk sharing, Takaful, and longevity risk sharing through tontines. These applications are treated within the same general framework, making it possible to compare mechanisms that are often studied separately in the actuarial literature.

The book is intended for advanced actuarial students, doctoral students, researchers, and practitioners interested in modern risk-sharing theory and decentralized forms of insurance. It is currently being written and is expected to be completed in June 2027.