Necessary and sufficient conditions of existence and uniqueness of solutions to integral equations of actuarial mathematics

Authors:
B. V. Norkin
Affiliations:
Institute of Program Systems of NANU, Kiev, Ukraine
Venue:
Cybernetics and Systems Analysis
Year:
2006

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Abstract

Necessary and sufficient conditions of existence and uniqueness of solutions of integral equations are established for ruin probability as a function of the initial capital of an insurance company. Several sufficient conditions and correctness conditions of the problem of finding ruin probability are also established. A general method of successive approximations for solution of this problem is substantiated.