Common Poisson shock models: applications to insurance and credit risk modelling. (English) Zbl 1087.91030
The paper deals with a methodologiacal approach suitable to analyse several types of losses, in particular insurance losses as well as losses related to the default in credit risk modelling.
The authors propose a general Poisson shock model, with arbitrary dimension and not-necessarily fatal shocks. Then the multivariate distribution of loss frequencies is studied, with particular attention to shock structure modeling.
Successively, this kind of analysis is developed by including dependent loss severities, by means of copula techniques. Several examples in insurance context as well as in credit risk modelling illustrate and clarify the results.
The authors propose a general Poisson shock model, with arbitrary dimension and not-necessarily fatal shocks. Then the multivariate distribution of loss frequencies is studied, with particular attention to shock structure modeling.
Successively, this kind of analysis is developed by including dependent loss severities, by means of copula techniques. Several examples in insurance context as well as in credit risk modelling illustrate and clarify the results.
Reviewer: Emilia Di Lorenzo (Napoli)
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 91G40 | Credit risk |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 62N05 | Reliability and life testing |
References:
| [1] | Risk Management: Value at Risk and Beyond (2001) |
| [2] | Modelling dependent defaults (2001) |
| [3] | Statistical Theory of Reliability and Life Testing (1975) · Zbl 0379.62080 |
| [4] | Insurance: Mathematics and Economics 22 pp 235– (1998) |
| [5] | DOI: 10.1017/S0021900200041024 · doi:10.1017/S0021900200041024 |
| [6] | Stochastic Processes for Insurance and Finance (1998) |
| [7] | DOI: 10.1017/S0515036100006796 · doi:10.1017/S0515036100006796 |
| [8] | An Introduction to Copulas (1999) |
| [9] | Journal of Finance 29 pp 449– (1974) |
| [10] | DOI: 10.1080/01621459.1967.10482885 · doi:10.1080/01621459.1967.10482885 |
| [11] | DOI: 10.1006/jmva.2000.1906 · Zbl 0982.60008 · doi:10.1006/jmva.2000.1906 |
| [12] | Multivariate Models and Dependence Concepts (1997) · Zbl 0990.62517 |
| [13] | On Default Correlation A Copula Function Approach (1999) |
| [14] | Journal of Finance L pp 1– (1995) |
| [15] | Loss Distributions (1984) |
| [16] | (1998) |
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