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Basic Life Insurance Mathematics

BasicLifeInsuranceMathematicsRagnarNorbe rgVersion:September 2002 Contents1 .. tcontracts:Surplusandbonus..172 Payment nitionsandrelationships.. loans..253 .. laws..374 Insuranceof a Insurance .. equivalence.. reserves.. 'sdi erentialequation.. distributions.. of view..575 singlelifeinsurancepolicy..626 of survivors..631 CONTENTS27 Markov chainsin a stochasticprocess.. chain.. revisited.. of present values.. Markov chaininterestmodel.. model.. erentialequationsformoments of present values.. onMarkov chains.. lives .. positive dependence.. values.. Markov chainmodelfortwo lives.

1.1 Banking versus insurance A. The bank savings contract. Upon celebrating his 55th anniversary Mr. (55) (let us call him so) decides to invest money to secure himself economically in his old age. The rst idea that occurs to him is to deposit a capital of S0 = 1 (e.g. one hundred thousand pounds) on a savings account today and draw the

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