Merton Problem in Insurance
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2022-03
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Abstract
The goal of Insurance companies, like that of any other financial institution, is to maximize their wealth. In doing so, there are different parameters they have to consider, such as premium rate, number of claim arrivals, size of claim arrival, etc. Moreover, they can invest their money in risk-free and risky asset to earn some income from those resources as well. This thesis discusses the application of Merton problem in insurance and risk and how to solve it. That is, we design a trading strategy for an insurance company such that its utility is maximized over a given time horizon. We use General Compound Hawkes Process to model the insurance’s risk and use the corresponding diffusion approximation to approximate the risk using a diffusion process. Then, we proceed with solving the problem by Hamilton- Jacobi-Bellman equation. Finally, we show some simulation results based on the calibration on data from insurance companies in Germany and their interpretations.
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Fooladamoli, E. (2022). Merton problem in insurance (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.