scholarly journals Modeling and Generating Dependent Risk Processes for IRM and DFA

2004 ◽  
Vol 34 (02) ◽  
pp. 333-360 ◽  
Author(s):  
Dietmar Pfeifer ◽  
Johana Nešlehová
Keyword(s):  
Financial Analysis ◽  
Great Part ◽  
Risky Assets ◽  
Collective Risk ◽  
Claim Number ◽  
Integrated Risk ◽  
Complex Dependence ◽  
Realistic Description ◽  
Risk Processes ◽  
Poisson Type

Modern Integrated Risk Management (IRM) and Dynamic Financial Analysis (DFA) rely in great part on an appropriate modeling of the stochastic behavior of the various risky assets and processes that influence the performance of the company under consideration. A major challenge here is a more substantial and realistic description and modeling of the various complex dependence structures between such risks showing up on all scales. In this presentation, we propose some approaches towards modeling and generating (simulating) dependent risk processes in the framework of collective risk theory, in particular w.r.t. dependent claim number processes of Poisson type (homogeneous and non-homogeneous), and compound Poisson processes.

scholarly journals Modeling and Generating Dependent Risk Processes for IRM and DFA

2004 ◽  
Vol 34 (2) ◽  
pp. 333-360 ◽  
Author(s):  
Dietmar Pfeifer ◽  
Johana Nešlehová
Keyword(s):  
Financial Analysis ◽  
Great Part ◽  
Risky Assets ◽  
Collective Risk ◽  
Claim Number ◽  
Integrated Risk ◽  
Complex Dependence ◽  
Realistic Description ◽  
Risk Processes ◽  
Poisson Type

Modern Integrated Risk Management (IRM) and Dynamic Financial Analysis (DFA) rely in great part on an appropriate modeling of the stochastic behavior of the various risky assets and processes that influence the performance of the company under consideration. A major challenge here is a more substantial and realistic description and modeling of the various complex dependence structures between such risks showing up on all scales. In this presentation, we propose some approaches towards modeling and generating (simulating) dependent risk processes in the framework of collective risk theory, in particular w.r.t. dependent claim number processes of Poisson type (homogeneous and non-homogeneous), and compound Poisson processes.

scholarly journals Analytical steps towards a numerical calculation of the ruin probability for a finite period when the riskprocess is of the Poisson type or of the more general type studied by Sparre Andersen

1971 ◽  
Vol 6 (1) ◽  
pp. 54-65 ◽  
Author(s):  
Olof Thorin
Keyword(s):  
Distribution Function ◽  
Numerical Calculation ◽  
Characteristic Function ◽  
Ruin Probability ◽  
Actuarial Science ◽  
Present Stage ◽  
Collective Risk ◽  
Finite Period ◽  
Stop Loss ◽  
Poisson Type

As is well-known, in the early 60's a Swedish committee set to work at the numerical calculation of the distribution function of the total amount of claims and of the related stop loss premiums in the Poisson and Polya cases (Bohman and Esscher [6]). Since the characteristic function for the said distribution function was easily available in terms of the characteristic function for the distribution function of an individual claim, the committee chose to base the numerical calculations on the C-method by H. Bohman (Bohman [5]). The calculation of the ruin probability for a finite or infinite period was not considered by the committee.The last-mentioned problem has now been taken up by a new committee formed by the Swedish Council for Actuarial Science and Insurance Statistics. The committee—consisting of H. Bohman, J. Jung, N. Wikstad and the present author—has to consider several aspects of the practical applicability of the collective risk theory. However, without possibilities of calculating—at least approximately—the ruin probability for a finite period the applicability of the existing ruin theories seems to be rather limited, so the committee has looked around for such possibilities. At the present stage the committee is considering the classical Poisson theory and Sparre Andersen's generalization of this theory [2]. It is the hope of the committee that, at a later stage, also the Polya theory and the theory recently presented by Segerdahl [11] combining the Sparre Andersen theory and the Polya theory may be treated.

scholarly journals Exemplification of Ruin Probabilities

1971 ◽  
Vol 6 (2) ◽  
pp. 147-152 ◽  
Author(s):  
Nils Wikstad
Keyword(s):  
Risk Process ◽  
Ruin Probabilities ◽  
Collective Risk ◽  
Fire Insurance ◽  
Finite Period ◽  
The Individual ◽  
Image Position ◽  
First Moment ◽  
Skew Distribution ◽  
Poisson Type

The following numerical values of ruin probabilities, Ψ(u, T) for finite times T, have been calculated by the method proposed in “Analytical steps towards a numerical calculation of the ruin probability for a finite period when the risk process is of the Poisson type or of the more general type studied by Sparre Andersen”, presented to this colloquium by Olof Thorin. The notations used in the sequel follow those of Thorin.Two distributions of the individual claims are considered, viz.,The latter distribution is a rather crude attempt to interprete the extremely skew distribution (Swedish non-industry fire insurance 1948-1951) considered by Cramér in his treatise “Collective Risk Theory”, Jubilee volume of Försäkringsaktiebolaget Skandia (1955) pp. 43-45.Likewise two distributions of the interoccurence times are considered, viz.,The d.f.B was considered by Sparre Andersen (TICA 1957 vol. II pp. 225-227).Note that the first moment equals one in all the d.f. mentioned.Though the analytical machinery also seems to work for o ≤ c ≤ 1 the Ψ values are indicated only for some values of c > 1. As known from Thorin's paper c stands for 1 + λ, where λ is the premiumloading, which means that for c = o Ψ(u, T) corresponds to the tail of the d.f. for the total amount of claims during the period (o, T).

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