ON THE APPLICATION OF THIELES DIFFERENTIAL-EQUATION IN LIFE-INSURANCE

Thiele's differential equation in the Markov chain model of life contingencies is used to derive formulas concerning the expected actual development of the mathematical reserve and accumulation of surplus for a (closed) insurance portfolio. Moreover formulas are developed for the insurance technical analysis of changes in the mathematical reserves for a single policy and for a (closed) insurance portfolio caused by alterations in the technical basis. The results are fundamental for investigating security aspects concerning the policy and insurance portfolio level. Finally the connection between our results and a counting process approach are discussed.