Discrete-time financial surplus models for insurance companies

• Autorzy: Helena Jasiulewicz
• Języki publikacji: EN

Abstrakty

EN

This paper reviews available discrete-time surplus models and results concerning the ruin probability and the distribution of random variables related to the time of ruin in the discussed models. The following models are presented: compound binomial risk model with independent and dependent claims, Sparre Andersen model of surplus process with independent and dependent claims, and models allowing for surplus investment. The review covers works discussing continuous model approximations using discrete models.(original abstract)

W artykule dokonano przeglądu znanych w literaturze modeli procesu nadwyżki w czasie dyskretnym i uzyskanych wyników dotyczących prawdopodobieństwa ruiny i rozkładów zmiennych losowych związanych z czasem ruiny w omawianych modelach. Zostały przedstawione: złożone dwumianowe modele ryzyka z niezależnymi i zależnymi roszczeniami, model Sparre Andersena procesu nadwyżki z niezależnymi i zależnymi roszczeniami oraz modele uwzględniające inwestowanie nadwyżki. Omówione zostały prace, w których rozważane są aproksymacje modeli ciągłych w czasie przez modele dyskretne. (abstrakt oryginalny)

Słowa kluczowe

EN

Investing; Enterprises financial evaluations models; Risk assessment

PL

Inwestowanie; Model oceny finansów przedsiębiorstwa; Ocena ryzyka

• Czasopismo: Roczniki Kolegium Analiz Ekonomicznych / Szkoła Główna Handlowa
• Rocznik: 2010
• Numer: nr 21 Zagadnienia aktuarialne : teoria i praktyka
• Strony: 225--255

Twórcy

autor

Helena Jasiulewicz

• Uniwersytet Przyrodniczy we Wrocławiu

Bibliografia

• N. L. Bowers, H. U. Gerber, J. C. Hickman, D. A. Jones, C. J. Nesbitt. Actuarial Mathematics. Society of Actuaries, Schaumburg, 1986.
• J. Cai, D. C. M. Dickson. Ruin probabilities with a Markov chain interest model. Insurance Math. Econom., 35:513-525, 2004.
• Y. Chen, C. Su. Finite time ruin probability with heavetailed insurance and financial risks. Insurance Math. Econom., 76:1812-1820, 2006.
• S. Cheng, H. U. Gerber, E. S. W. Shiu. Discounted probabilities and ruin theory in the compound binomial model. Insurance Math. Econom., 26:239-250, 2000.
• H. Cosette, D. Landriault, E. Marceau. Ruin probabilities in the compound Markov binomial model. Scand. Actuarial J., 4:301-323, 2003.
• H. Cosette, D. Landriault, E. Marceau. Compound binomial risk model in a markouian enuironment. Insurance Math. Econom., 35:425-443, 2004.
• H. Cosette, D. Landriault, E. Marceau. Exact ezpression and upper boundfor ruin probabilities in the compound Markov binomial model. Insurance Math. Econom.,34:449-466, 2004.
• H. Cosette, D. Landriault, E. Marceau. Ruin probabilities in the discrete renewal risk model. Insurance Math. Econom., 38:309-323, 2006.
• T. G. de Kok. Ruin probabilities with compounding assets for discrete time finite horizon problems, independent period claim sizes and generał premium structure. Insurance Math. Econom., 33:645-658, 2003.
• D. C. M. Dickson. Some comments on the compound binomial model. ASTIN Bulletin, 24:33-45, 1994.
• L. Gajek. On the deficit distribution when ruin occurs-discrete time model. Insurance Math. Econom., 36:13-24, 2005.
• H. U. Gerber. Mathematical fun with ruin theory. Insurance Math. Econom., 7:15-23, 1988.
• H. U. Gerber. Mathematical fun with the compound binomial process. ASTIN Bulletin, 18:161-168, 1988.
• A. Groniowska, W. Niemiro. Controlled risk processes in discrete time: Lower and upper approximation to the optimal probability of ruin. Insurance Math. Econom., 36:433-440, 2005.
• S. Heilpern. Funkcje łączące - podstawowe pojęcia i własności. Wyd. AE, Wrocław, 2007.
• H. Jasiulewicz. Proces rezerwy w czasie dyskretnym z losową stopą procentową i losową składką. Konferencja Aktuarialna, 2008.
• N. L. Johnson, S. Kotz., Balakrishnan. Discrete Multwariate Distribution. Wiley, New yok, 1997.
• S. Kocherlakota, L. Kocherlakota. Bivariate Discrete Distribution. Marcel Dekker, New York, 1992.
• S. Li. Distribution ofthe surplus before ruin, the deficit at ruin and the claim causing ruin in a class of discrete time risk models. Scand. Actuarial J., 4:271-284, 2005.
• S. Li. On a class of discrete time renewal risk models. Scand. Actuarial J., 4:241-260, 2005.
• S. Li, J. Garrido. On the time value ofruin in the discrete time risk model. Departamento de Economia de la Empressa, Universidad Carlos III de Madrid, Working Paper 02-18, Business Economic Series 12, 2002.
• G. Liu, Y. Wang, B. Zhang. Ruin probability in the continuous-time compound binomial model. Insurance Math. Econom., 36:303-316, 2005.
• G. Liu, J. Zhao. Joint distributions of some actuarial random vector in the compound binomial model. Insurance Math. Econom., 40:95-103, 2007.
• E. Marceau. On the discree-time compound reneual risk model with dependence. Insurance Math. Econom., 44:245-259, 2009.
• R. Nelsen, An Introduction to Copulas. Springer, New York, 1999.
• H. Nyrhinen. On the ruin probabilities in a generał economic enuironment. Stochastic Processes Appl., 83:319-330, 1999.
• H. Nyrhinen. Finite and infinite ruin probabilities in stochastic economic environment. Stochastic Processes Appl., 92:265-285, 2001.
• K. P. Pavlova, G. E. Willmot. The discrete stationary renewal risk model and the gerber-shiu discounted penalty function. Insurance Math. Econom., 35:467-277, 2004.
• J. M. Reihard, M. Snoussi. On the distribution of the surplus prior to ruin in a discrete semi-Maarkov risk model. ASTIN Bulletin, 31:255-273, 2001.
• J. M. Reinhard, M. Snoussi. The severity of ruin in a discrete semi Markov risk model. Commun. Statist.-Stochastic Models, 18:85-107, 2002.
• J. M. Reinhard, M. Snoussi. A monotonically conuerging algorithm for the seuerity of ruin in a discrete semi-markov risk model. Scand.' Actuarial J., 5:336-354, 2004.
• M. Schal. On discrete-time dynamie programming in insurance:exponential utitlty and mimizing the ruin probability. Scand. Actuarial J., 3:189-201, 2004.
• E. S. W. Shiu. The probability of euentual ruin in the compound binomial model. ASTIN Bulletin, 19:179-190, 1989.
• Q. Tang. The ruin probability of a discrete time risk model under constant interest rate with heavy tails. Scand. Actuarial J., 3:229-240, 2004.
• Q. Tang, G. Tsitsiashvili. Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risk. Stochastic Procęsses Appl., 108:299-325, 2003.
• F. D. Vylder. Advanced Risk Theory: A self-contained Introduction. Editions de Universite de Bruxelles, Brussels, 1996.
• G. E. Willmot. Ruin probabilities in the compound binomial model. Insurance Math. Econom., 12:133-142, 1993.
• G. E. Willmot, J. Cai. Aging and other distributional properties of discrete compound geometrie distributions. Insurance Math. Econom., 28:361-379, 2001.
• H. Yang, L. Zhang. Ruin problems for a discrete time risk model with random interest rate. Math. Meth. Oper. Res, 63:287-299, 2006.
• K. C. Yuen, J. Y. Guo. Ruin probabilities for time-correlated claims in the compound binomial model. Insurance Math. Econom., 29:47-57, 2001.