Valuation and risk management in life insuranceVom Fachbereich Mathematik derTechnischen Universit¨at Darmstadtzur Erlangung des Grades einesDoktors der Naturwissenschaften(Dr. rer. nat.) genehmigteDissertationvonDipl.-Math. Tom Fischeraus Heilbronn-NeckargartachReferent: Prof. Dr. J. LehnKorreferent: Prof. Dr. U. RiederTag der Einreichung: 30. Oktober 2003Tag der mu¨ndlichen Pru¨fung: 5. Februar 2004Darmstadt 2004D 172Certainformsofuncertaintymakelifeinterestingbutlesssafe. Iwasalwaysintriguedbythevariousformsofriskthatareassociatedwith human life and activity and how they can be mitigated forthe individual by contractual risk exchange between two or moreparties. Certain forms of certainty make life interesting and moresafe. I was always attracted to mathematics because it allows ofstatements that are non-trivial and still indisputably true. Thesetwo areas of interest synthesize perfectly into actuarial/financialmathematics, which gives precise contents to notions of risk anddevelops methods for measuring and controlling it. [...]Ragnar Norberg3Preliminary remarkLife insurance mathematics is perhaps the most interesting and challengingfield at the interface of modern actuarial and financial mathematics. It isthe intention of this Ph.D. thesis to examine and understand some particularaspects of modern life insurance which have not yet been sufficiently consid-ered.