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This introductory course deals with the mathematical fundamentals of life-, health- and pension-insurance. In particular, this course serves as an introduction to actuarial science / insurance economics. It covers basic probabilistic models  for the computation of future lifetimes and life-tables, actuarial present values, expected payoffs and safety margins. The course discusses:

• the calculation of premiums (principle of equivalence) for immediate and deferred life annuities, pure endowment, life insurance, health insurance and corporate pension schemes
• the calculation of actuarial reserves
• the distribution of surpluses.

This lecture is accredited by the German actuarial society (Deutsche Aktuar Vereinigung DAV) as passing its exam in insurance mathematics ("Versicherungsmathematik").

The requirements for accreditation are passing this course and "Risk Theory 2", which will be offered in the next summer semester.

Passing the exams of the DAV is a crucial requirement for becoming a member of the DAV. The accreditation of university courses as DAV exams offers to all students wishing to work in this field (e.g. insurance companies, consulting firms, auditing firms or building societies) the immense advantage that they are enabled to pass DAV exams during their regular study (and not parallel to their work) - an important bonus for the start of their career.

The lecture is oriented at Bachelor and Master students of all fields with a major in mathematics or economics.
Prerequisites are (advisable but not mandatory):

• „Elementare Wahrscheinlichkeitsrechnung und Statistik“  (WiMa) or „Stochastik und Wirtschaftsstatistik“ (WiWi) (or comparable knowledge of probability theory)
• „Externes Rechnungswesen“ or comparable knowledge of  accounting

The course does not closely follow a specific literature, but the following literature captures some aspects which we discuss in the lecture.

Life-, Health- and Pension-Mathematics:

• Dickson, C.M., M.R. Hardy, H.R. Waters, Actuarial Mathematics for Life Contingent Risks, 2nd ed., 2013, Cambridge University Press, Cambridge
• Führer, C., Grimmer, A.: Einführung in die Lebensversicherungsmathematik, 2010, HG 8781/2010 F
• Neuburger, E.: Mathematik und Technik betrieblicher Pensionszusagen, 1997, HG 8781/1997 N
• Neuburger, E.: Formeln der Pensionsversicherungsmathematik

Health Insurance Mathematics:

• Milbrodt, H.: Aktuarielle Methoden der deutschen Privaten Krankenversicherung, 2005, HG 8781/2005 Mb
• Bohn, K.: Die Mathematik der deutschen privaten Krankenversicherung, 1980, HG 8781/A1.11