Minimizing The Probability Of Ultimate Ruin By Proportional Reinsurance And Investments

The study was conducted on the topic: Minimizing the Probability of Ultimate Ruin by Proportional Reinsurance and Investments. The purpose of the study was to determine the role of investments in minimizing the probability of ultimate ruin of an insurance company, to assess the impact of proportional reinsurance on the survival of insurance companies as well as to determine the optimal reinsurance percentage b (0, 1].

The study considered a risk process comprising a diffffusion-perturbated insurance process and a diffffusion-perturbated investment generating process in which invest ments were modelled as a Black-Scholes model. The Hamilton-Jacobi-Bellman (HJB) equation for this problem was derived, as well as its corresponding Volterra integro difffferential equation which was then tranformed into a linear Volterra integral equa tion of the second kind. This integral equation was then solved using the block-by block numerical method for the retention percentage that minimizes the probability of ultimate ruin. The major fifindings of this study were as follows:
1. That, as expected, the higher the investment rate, the lower the ruin probabil
ity. Furthermore, the study has revealed that volatility of stock prices results
in higher ruin probabilities.
2. That for a given initial surplus, the ruin probabilities keep reducing as the value
of the retention level b reduces. After a certain b, however, the ruin probabilities
begin rising again, giving an indication of the location of the optimal retention
percentage .
Subscribe to access this work and thousands more
Overall Rating

0

5 Star
(0)
4 Star
(0)
3 Star
(0)
2 Star
(0)
1 Star
(0)
APA

Kasumo, C (2021). Minimizing The Probability Of Ultimate Ruin By Proportional Reinsurance And Investments. Afribary. Retrieved from https://tracking.afribary.com/works/minimizing-the-probability-of-ultimate-ruin-by-proportional-reinsurance-and-investments

MLA 8th

Kasumo, Christian "Minimizing The Probability Of Ultimate Ruin By Proportional Reinsurance And Investments" Afribary. Afribary, 12 May. 2021, https://tracking.afribary.com/works/minimizing-the-probability-of-ultimate-ruin-by-proportional-reinsurance-and-investments. Accessed 07 Nov. 2024.

MLA7

Kasumo, Christian . "Minimizing The Probability Of Ultimate Ruin By Proportional Reinsurance And Investments". Afribary, Afribary, 12 May. 2021. Web. 07 Nov. 2024. < https://tracking.afribary.com/works/minimizing-the-probability-of-ultimate-ruin-by-proportional-reinsurance-and-investments >.

Chicago

Kasumo, Christian . "Minimizing The Probability Of Ultimate Ruin By Proportional Reinsurance And Investments" Afribary (2021). Accessed November 07, 2024. https://tracking.afribary.com/works/minimizing-the-probability-of-ultimate-ruin-by-proportional-reinsurance-and-investments

Document Details
Christian Kasumo Field: Mathematics Type: Exam Question 100 PAGES (21997 WORDS) (pdf)