Surplus Analysis of Sparre Andersen Insurance Risk Processes

Gordon E. Willmot is Munich Re Chair in Insurance and professor in the Department of Statistics and Actuarial Science at the University of Waterloo, Canada. His research interests are in stochastic modelling in insurance. Willmot has (co-)authored over one hundred research papers in leading actuarial and statistical journals. He is also co-author of Lundberg Approximations for Compound Distributions with Insurance Applications (Springer), Loss Models - From Data to Decisions and Loss Models - Further Topics (Wiley), and Insurance Risk Models (Society of Actuaries). He is editor of Insurance: Mathematics and Economics.Jae-Kyung Woo is Associate Professor in the School of Risk and Actuarial Studies at the University of New South Wales, Sydney. She has worked at the University of Hong Kong and Columbia University prior to joining UNSW. Her research interests are focused on risk theory, reliability theory, aggregate claim analysis,and queueing theory. She has published about twenty papers dealing with the subject of the present monograph and related topics.

“The monograph is devoted to the surplus analysis of the Sparre-Andersen process using the renewal process as the model for claim counts. … This book is intended for researchers interested in ruin/risk theory, and will also be useful for graduate students specialized in classical and modern risk theory.” (Anatoliy Swishchuk, zbMATH 1391.91006, 2018)

• 1 Introduction.- 2 Technical Preparation.- 3 Gerber–Shiu Analysis in the Classical Poisson Risk Model.- 4 Gerber–Shiu Analysis in the Dependent Sparre Andersen Model.- 5 Models Involving Erlang Components.- 6 The Time of Ruin in the Classical Poisson Risk Model.- 7 Related Risk Models.- 8 Other Topics.- References.- Index.