Minimizing The Probability Of Ultimate Ruin By Proportional Reinsurance And Investments

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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 b ∗.

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Minimizing The Probability Of Ultimate Ruin By Proportional Reinsurance And Investments

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