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Information × Registration Number 0210U005617, 0110U000829 , R & D reports Title The investigation of actuarial integral equation and their application to extmation of risk of finantial institution bunkrupcy. popup.stage_title Head Norkin Bogdan Volodymyrovich, Registration Date 22-12-2010 Organization V.M.Glushkov Institute of Cybernetics of NASU popup.description2 In the project various generalizations of the classical risk process describing a stochastic evolution of the capital of an insurance company are proposed. In particular risk processes with variable deterministic premiums, with random premiums, with non Poisson flows of premiums and claims, risk processes in a stochastic markovian environment are studied. Such processes may also describe a stochastic evolution of a capital of a bank or other financial institution. Integral equations for the probability of nonruin as a function of the initial capital of the company for various generalizations of the classical risk process are deduced. For a risk process in a stochastic markovian environment system of integral equations for a set of nonruin probabilities from various initial states of the process are obtained. A successive approximation method for a numerical or analytical solution of the considered integral equations of insurance mathematics is theoretically and practically validated, a stochastic version of the method is proposed. A technique of estimation of the accuracy of approximate solutions of considered integral equations is developed by construction of approximations to the exact solution from above and from below. Product Description popup.authors Норкін Богдан Володимирович popup.nrat_date 2020-04-02 Close