An optimization approach to adaptive multi-dimensional capital management |
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Institution: | 1. Korteweg–de Vries Institute for Mathematics, University of Amsterdam, Science Park 107, 1098 XH Amsterdam, The Netherlands;2. Rabobank, Croeselaan 18, 3521 CB Utrecht, The Netherlands;3. CWI - National Research Institute of Applied Mathematics and Computer Science, Science Park 123, 1098 XG Amsterdam, The Netherlands;4. Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands |
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Abstract: | Firms should keep capital to offer sufficient protection against the risks they are facing. In the insurance context methods have been developed to determine the minimum capital level required, but less so in the context of firms with multiple business lines including allocation. The individual capital reserve of each line can be represented by means of classical models, such as the conventional Cramér–Lundberg model, but the challenge lies in soundly modelling the correlations between the business lines. We propose a simple yet versatile approach that allows for dependence by introducing a common environmental factor. We present a novel Bayesian approach to calibrate the latent environmental state distribution based on observations concerning the claim processes. The calibration approach is adjusted for an environmental factor that changes over time. The convergence of the calibration procedure towards the true environmental state is deduced. We then point out how to determine the optimal initial capital of the different business lines under specific constraints on the ruin probability of subsets of business lines. Upon combining the above findings, we have developed an easy-to-implement approach to capital risk management in a multi-dimensional insurance risk model. |
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Keywords: | Ruin probability Insurance risk Bayesian statistics Optimal allocation Multi-dimensional risk process |
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