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Tytuł artykułu
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Warianty tytułu
Asymptotics of Ruin Probability for Risk Processes under Investment and Reinsurance StrategieR
Języki publikacji
Abstrakty
Prawdopodobieństwo ruiny jest jednym z głównych problemów związanych z teorią ryzyka. Wzory analityczne są znane tylko w kilku szczególnych przypadkach. Dlatego w celu oszacowania tego prawdopodobieństwa stosuje się różnego typu symulacje komputerowe, aproksymacje oraz asymptotyki. Zaprezentowano asymptotykę prawdopodobieństwa ruiny w kilku różnych modelach. Zanalizowano wpływ inwestycji i reasekuracji na prawdopodobieństwa ruiny.
Ruin probability is one of the main problems related to risk theory. We are able to calculate it only in a few cases. So we are interested in its asymptotics. In this article, we will present the asymptotics of the ruin probability in several different models. We will analyze the influence of investment and reinsurance on ruin probability. (original abstract)
Rocznik
Strony
56--68
Opis fizyczny
Twórcy
autor
- Akademia Ekonomiczna we Wrocławiu
Bibliografia
- Asmussen S., Ruin Probabilities, World Scientific, Singapore 2000.
- Maid M.. Schmidli I I., On the maximisation of the adjustment coefficient under proportional reinsurance, „Astin Bulletin" 2004, vol. 34, no. 1.
- Hipp C., Stochastic control with application in Insurance, [w:] Stochastic Methods in Finance, „Lecture Notes in Mathematics", vol. 1856, Springer-Verlag, Berlin 2004, s. 127-164.
- Hipp C., Schmidli H., Asymptotics of ruin probabilities for controlled risk processes in the small claims case, „Scandinavian Actuarial Journal" 2004, no. 5.
- Hipp C„ Vogt M„ Optimal dynamic XL reinsurance, „Astin Bulletin" 2003, vol. 33, no. 2.
- Kwaśniewska M., Optimal investment and XL reinsurance, „Mathematical Economics" 2005, no. 9.
- Rolski T., Schmidli H., Schmidt V., Teugels J., Stochastic Processes for Insurance and Finance, Wiley, New York 1999.
- Schmidli H., Characteristics of ruin probabilities in classical risk models with and without investment. Cox risk models and perturbed risk models. Preprint, 2000.
- Schmidli H., Optimal proportional reinsurance policies in a dynamic setting, „Scandinavian Actuarial Journal" 2001, no. 1.
- Schmidli H., Asymptotics of ruin probabilities for risk processes under optimal reinsurance policies: the small claim case, Working Paper 180, Laboratory of Actuarial Mathematics, University of Copenhagen, 2002.
- Schmidli H., On minimizing the ruin probability by investment and reinsurance, „Annals of Applied Probability" 2002, vol. 12, no. 3.
- Schmidli IL, On Cramer-Lundberg approximations for ruin probabilities under optimal excess of loss reinsurance, Working Paper 193, Laboratory of Actuarial Mathematics, University of Copenhagen, 2004.
- Schmidli H., Asymptotics of ruin probabilities for risk processes under optimal reinsurance and investment policies: the large claim case, „Queueing Systems" 2004, no. 46.
- Schmidli H., Optimisation in non-life insurance, „Stochastic Models" 2006, vol. 22, no. 4.
- Waters H.R., Some mathematical aspects of reinsurance, „Insurance: Mathematics and Economics" 1983, no. 2.
Typ dokumentu
Bibliografia
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