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Essays on Capital Calculation in Insurance

Master's Thesis
Corporate Partner: 
Date Published: 
March 30, 2017
In order to be able to bear the risk they are taking, insurance companies have to set aside a certain amount to guarantee the payment of liabilities, up to a defined probability, thus remaining solvent should unwanted events occur. This amount is referred to as capital. The calculation of capital is a complex problem. To be sustainable, capital must consider all possible risk sources that might lead to losses of assets, and the liabilities of the insurance company, and it must account for the likelihood and the effect of these bad (and usually extreme) events, which could occur due to these sources of risk. Insurance companies build models and tools to perform this capital calculation. To do so, they have to collect data, build statistical evidence, and build mathematical models and tools in order to efficiently and accurately derive capital. This thesis deals with three major difficulties. First, the uncertainty behind the choice of a specific model and the quantification of this uncertainty in terms of additional capital. The use of external scenarios—that is to say, opinions with regard to the likelihood of certain events happening, allows one to build a coherent methodology that make the capital cushion more robust with regard to a wrong specification of the model in question. Second, the computational complexity of using these models in an industrialized environment, and numerical methods available for increasing their computational efficiency. Most of these models cannot provide an analytical formula of capital. Consequently, one has to approx- imate it via simulation methods. Considering the high number of risk sources and the complexity of insurance contracts, these methods can be slow to run until they provide reasonable accuracy. This often makes the models unusable in practical terms. Enhancements of classical simulation methods are presented with the aim of making these approximations faster to run for the same level of accuracy. Third, the lack of reliable data and the high complexity of problems with long time horizons, and statistical methods for identifying and building reliable proxies in such cases. A typical example is life-insurance contracts that imply being exposed to multiple risk sources over a long horizon. Such contracts can, in fact, be approximated wisely by proxies that can capture risk over time.