The approximate solution of advanced stochastic timedelay differential equations using block Adams Moulton methods and its application in claims settlement for policyholders satisfaction in the Nigerian insurance industry

Abstract

In this paper, Block Adams Moulton Methods (BAMM) is implemented for the approximate solution of Advanced Stochastic Time-Delay Differential Equations (ASTDDEs) to determine the level of policyholders’ satisfaction in settling their claims in Nigerian Insurance Industry. With the help of continuous development of multistep collocation method by matrix inversion techniques, the discrete schemes of the proposed method (BAMM) were derived. The analysis of basic properties of the method such as order and error constant, consistency, zero stability, convergence and region of absolute stability were carried-out and proved satisfactory. The numerical solutions of the method were obtained, computed and presented graphically by solving some advanced stochastic time-delay differential equations using the derived discrete schemes which revealed the effect of advanced stochastic time-delay on the policyholders’ claims settlement. The accuracy of the method was examined by comparing the results obtained with other existing methods and was found to give better approximation.