University essay from Umeå universitet/Institutionen för matematik och matematisk statistik

Abstract: Cyber attacks against companies are becoming more common as technology advances and digitalization is increasing exponentially. All Swedish insurance companies that sell cyber insurance encounter the same problem, there is not enough data to do good actuarial work. In order for the pricing procedure to improve and general knowledge of cyber insurance to increase, it has been proposed that insurance companies should share their data with each other. The goal of the thesis is to do mathematical calculations to explore data quality consequences of such a sharing regime. This thesis is based on some important assumptions and three scenarios. The most important assumptions are that there are two insurance companies forced to share all their data with each other and that they can reduce the uncertainty about their own product by investing in better data quality. In the first scenario, we assume a game between two players where they can choose how much to invest in reducing the uncertainty. In the second scenario, we assume that there is not a game, but the two insurance companies are forced to equal investments and thus have the same knowledge of their products. In the third scenario, we assume that the players are risk averse, that is, they are not willing to take high risk. The results will show how much, if any, the insurance companies should invest in the different scenarios to maximize their profits (if risk neutral) or utility (if risk averse). The results of this thesis show that in the first and second scenario, the optimal profit is reached when the insurance companies do not invest anything. In the third scenario though, the optimal investment is greater than zero, given that the companies are enough risk averse.

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