An optimization approach to adaptive multi-dimensional capital management
| Autor: | Peter Spreij, G. A. Delsing, Michel Mandjes, Erik Winands |
|---|---|
| Přispěvatelé: | Stochastics (KDV, FNWI), Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Economics and Econometrics Computer science Ruin probability Bayesian probability Context (language use) Bayesian statistics 01 natural sciences FOS: Economics and business Insurance risk 010104 statistics & probability Convergence (routing) FOS: Mathematics Econometrics Minimum capital 0101 mathematics Risk management Optimal allocation business.industry Individual capital Probability (math.PR) 05 social sciences 050301 education Multi-dimensional risk process Risk Management (q-fin.RM) Capital (economics) Statistics Probability and Uncertainty business 0503 education Mathematics - Probability Quantitative Finance - Risk Management |
| Zdroj: | Insurance: Mathematics and Economics, 84, 87-97. Elsevier Insurance: Mathematics and Economics, 84, 87-97 |
| ISSN: | 1873-5959 0167-6687 |
| Popis: | 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 Cram\'{e}r-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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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