On Valuation and Control in Life and Pension Insurance

My interest in the topics dealt with in this thesis was aroused during my graduate studies and the preparation of my master's thesis. I realized a number of open questions and wanted to search for some of the answers. This search started with my master's thesis and continues with the present thesis. Chapter 2 is closely related to parts of my master's thesis. However, the framework and the results are generalized to such an extent that it can be submitted as an integrated part of this thesis. Each chapter is more or less self-contained and can be read independently from the rest. This prepares a submission for publication of parts of the thesis. Some parts have already been published. However, Chapters 3 and 4 build strongly on the framework developed in Chapter 2. For the sake of independence, they will both contain a brief introduction to this framework and a few motivating examples. Acknowledgments I wish to thank my supervisors Ragnar Norberg and Christian Hipp for their cheerful supervision during the last three years. I owe a debt of gratitude to Ragnar Norberg for shaping my understanding of and interest in various involved problems of insurance and financial mathematics and for encouraging me to go for the Ph.D. degree. Christian Hipp sharpened my understanding and I thank him for numerous fruitful discussions, in particular during my six months stay at University of Karls-ruhe. A special thank goes to Professor Michael Taksar, State University of New York at Stony Brook, for his hospitality during my three months stay at SUNY at Stony Brook. Despite no supervisory duties, he took his time for many valuable discussions on stochastic control theory. I also wish to thank my colleagues, fellow students, and friends for interesting dis-iii iv cussions and all their support. Finally, thanks to Jeppe Ekstrøm who, under my supervision, prepared a master's thesis from which the figures in Chapter 3 are taken. Summary This thesis deals with financial valuation and stochastic control methods and their application to life and pension insurance. Financial valuation of payment streams flowing from one party to another, possibly controlled by one of the parties or both, is important in several areas of insurance mathematics. Insurance companies need theoretically substantiated methods of pricing, accounting, decision making, and optimal design in connection with insurance products. Insurance products like e.g. endowment insurances with guarantees and bonus and surrender options distinguish …