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Branching, Ruin, Soccer

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Book cover Point Process Theory and Applications

Part of the book series: Probability and its Applications ((PA))

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Abstracts

In this chapter three quite different models are presented: a branching process for the evolution of a population with age-dependent birth and death intensities; a classical model from risk theory with a discussion of the problem of calculating the probability of ruin and the distribution of the time to ruin; a model for how a soccer game develops over time, using a simple multiplicative Poisson model as starting point.

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Chapter 9

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A branching process

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Ruin probabilities

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  2. Gerber, H.E. (1979). An Introduction to Mathematical Risk Theory. Huebner Foundation Monographs, Wharton School, Philadelphia.

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  3. Jacobsen, M. (2003). Martingales and the distribution of the time to ruin. Stoch. Proc. Appl. 107, 29–51.

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  4. Jacobsen, M. (2005). The time to ruin for a class of Markov additive processes. Adv. Appl. Probab. (to appear).

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  5. Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J. (1999). Stochastic Processes for Insurance and Finance. Wiley, New York.

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The soccer model

  1. Davison, A.C. (2003). Statistical Models.

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© 2006 Birkhäuser Boston

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(2006). Branching, Ruin, Soccer. In: Point Process Theory and Applications. Probability and its Applications. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4463-6_9

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