Minimizing the probability of ultimate ruin by excess of loss reinsurance and Investments
| dc.contributor.author | Joseph, Agnes | |
| dc.date.accessioned | 2019-10-31T09:27:20Z | |
| dc.date.accessioned | 2020-01-07T14:42:13Z | |
| dc.date.available | 2019-10-31T09:27:20Z | |
| dc.date.available | 2020-01-07T14:42:13Z | |
| dc.date.issued | 2013 | |
| dc.description | Available in print form, East Africana Collection, Dr. Wilbert Chagula Library, Class mark (THS EAF HG8083.J67) | en_US |
| dc.description.abstract | Insurance companies provide protection to individuals against possible unexpected losses. While insuring individual risks, the insurance company is itself exposed to a risk of its surplus becoming negative. Therefore in this research, we consider a risk management strategy where the insurance company chooses to re-insure its surplus under excess of loss reinsurance arrangement and invests into both risky and risk free assets.We model the wealth dynamics of an insurance company by a risk process perturbed by diffusion. This process is then compounded by another return on investment process of Black-Scholes type. These two processes combined, form the risk process used in this dissertation. The Hamilton-Jacob-Bellman equation for this problem is then derived as well as its corresponding Volterra Integra Differential Equation of the second kind which is then transformed into a linear Volterra Integral Equation of second kind. We solve this integral equation numerically using the block-by-block method for different retention levels for chosen parameters. The results show that, the higher the rate of investment, the lower the ruin probability. Furthermore, the study reveals that, for a given initial capital, the ruin probability keeps on declining as the retention level for reinsurance increases. However, after a certain level, the probabilities begin rising again, giving an indication of the optimal retention level for Excess of Loss reinsurance. | en_US |
| dc.identifier.citation | Joseph, A (2013) Minimizing the probability of ultimate ruin by excess of loss reinsurance and Investments.Master dissertation, University of Dar es Salaam, Dar es Salaam. | en_US |
| dc.identifier.uri | http://localhost:8080/xmlui/handle/123456789/613 | |
| dc.language.iso | en | en_US |
| dc.publisher | University of Dar es Salaam | en_US |
| dc.subject | Risk (Insurance) | en_US |
| dc.subject | Reinsurance | en_US |
| dc.subject | Mathematical models | en_US |
| dc.title | Minimizing the probability of ultimate ruin by excess of loss reinsurance and Investments | en_US |
| dc.type | Thesis | en_US |