Probability Tools For Stochastic Modelling -- Renewal Theory and Markov Chains -- Markov Renewal Processes, Semi-Markov Processes and Markov Random Walks -- Discrete Time and Reward Smp and their Numerical Treatment -- Semi-Markov Extensions of the Black-Scholes Model -- Other Semi-Markov Models in Finance and Insurance -- Insurance Risk Models -- Reliability and Credit Risk Models -- Generalised Non-Homogeneous Models for Pension Funds and Manpower Management.

This book presents applications of semi-Markov processes in finance, insurance and reliability, using real-life problems as examples. After a presentation of the main probabilistic tools necessary for understanding of the book, the authors show how to apply semi-Markov processes in finance, starting from the axiomatic definition and continuing eventually to the most advanced financial tools, particularly in insurance and in risk-and-ruin theories. Also considered are reliability problems that interact with credit risk theory in finance. The unique approach of this book is to solve finance and insurance problems with semi-Markov models in a complete way and furthermore present real-life applications of semi-Markov processes. Audience This book is intended for applied mathematicians, statisticians, financial intermediaries, actuaries, engineers, operations researchers.