Probability of ultimate survival is one of the central problems in insurance because it is a management tool that may be used to check on the solvency levels of the insurer. In this article, we numerically compute this probability for an insurer whose portfolio is compounded by investments arising from a risky asset. The uncertainty in the celebrated Cramér-Lundberg model is provided by a standard Brownian motion that is independent of the standard Brownian motion in the model for the risky asset. We apply an order four Block-by-block method in conjunction with the Simpson rule to solve the resulting Volterra integral equation of the second kind. The ultimate survival probability is arrived at by taking a linear combination of some two solutions to the Volterra equations. The several numerical examples show that the results are accurate and reliable. The method performs well even when the net profit condition is violated.
(R1503) Numerical Ultimate Survival Probabilities in an Insurance Portfolio Compounded by Risky Investments,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 17,
1, Article 4.
Available at: https://digitalcommons.pvamu.edu/aam/vol17/iss1/4