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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.. chains.. fertility analysis.. 1068 Probability distributionsof present .. probability distributionsof present valuesby ele-mentarymethods.

CHAPTER 1. INTRODUCTION 7 total savings after 15 years amount to L55 S15, which yields an individual share equal to L55 S15 L70 (1.3) to each of the L70 survivors if L70 >0. By the so-called law of large numbers, the proportion of survivors L70=L55 tends to the individual survival probability 0:75 as the number of participants L55 tends to in nity. Therefore, as the

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