TY  - JOUR
AU  - Kasozi, Juma 
AU  - Paulsen, Jostein 
PY  - 2005
TI  - Numerical Ultimate Ruin Probabilities under Interest Force
JF  - Journal of Mathematics and Statistics
VL  - 1
IS  - 3
DO  - 10.3844/jmssp.2005.246.251
UR  - https://thescipub.com/abstract/jmssp.2005.246.251
AB  - This work addresses the issue of ruin of an insurer whose portfolio is exposed to insurance risk arising from the classical surplus process. Availability of a positive interest rate in the financial world forces the insurer to invest into a risk free asset. We derive a linear Volterra integral equation of the second kind and apply an order four Block-by-block method in conjuction with the Simpson rule to solve the Volterra equation for ultimate ruin. This probability is arrived at by taking a linear combination of some two solutions to the Volterra integral equation. The several numerical examples given show that our results are excellent and reliable.