Models of Dependent Risk - Analysis of Probability of Ruin

• Autorzy: Stanisław Heilpern
• Języki publikacji: EN

Abstrakty

EN

The paper is devoted to the nonstandard risk processes included the dependent random variables. We present three models in it. The different dependent structure are investigated and the influence of the degree of dependence on the probability of ruin is studied. We can see, that there is not regularity in such influence in some cases. We also present the cases when we can exactly calculate the probability of ruin. The discrete risk process is investigated in the first model. The dependence of the interclaim time random variables is assumed, as opposed to the classical risk process done by Shiu [1989]. We present the recurrence formulas on the probability of ruin in the continuous case and in the Markovian case, when the interclaim time random variables create the Markov chain. The strict dependent case and the situation when the dependent structured described by Archimedean copula are studied. The second model is continuous. We take the more realistic assumption, that the claims may be dependent and we study the case when the dependent structure is described by copula. In the last model, the probability of ruin when the values of claim and the interclaim time may be dependent is studied. Two cases are investigated: continuous and discrete.(original abstract)

Słowa kluczowe

EN

Random variable; Enterprises bankruptcy forecasting; Markov chain

PL

Zmienne losowe; Prognozowanie upadłości przedsiębiorstwa; Łańcuch Markowa

• Czasopismo: Prace Naukowe / Uniwersytet Ekonomiczny w Katowicach
• Rocznik: 2011
• Tom: Mathematical, Econometrical and Computer Methods in Finance and Insurance 2009
• Strony: 68--81

Twórcy

autor

Stanisław Heilpern

• Wrocław University of Economics, Poland

Bibliografia

• Ambagaspitya R.S. (2009): Ultimate Ruin Probability in the Spare Andersen Model with Dependent Claim Sizes and Claim Occurrence Times. "Insurance: Mathematics and Economics", No. 44.
• Cossete H., Landriault D., Marceau E. (2004): Exact Expressions and Upper Bound for Ruin Probabilities in the Compound Markov Binomial Model. "Insurance: Mathematics and Economics", No. 34.
• Gerber E. (1988): Mathematical Fun with the Compound Binomial Process. "ASTIN Bulletin", No. 18.
• Heilpern S.: Zależny proces ryzyka, wyznaczanie prawdopodobieństwa ruiny. [w:] Statystyka Aktuarialna, Teoria i Praktyka. Red. W. Otto. Wydawnictwo Uniwersytetu Warszawskiego, Warszawa (w druku).
• Heilpern S., Modele zależnego ryzyka - wyznaczanie prawdopodobieństwa ruiny. "Badania Operacyjne i Decyzje", w recenzji.
• Kaas R., Goovaerts M., Dhaene J., Denuit M. (2001): Modern Actuarial Risk Theory. Kluwer, Boston.
• Marceau E. (2009): On the Discrete-time Compound Renewal Risk Model with Dependence. "Insurance: Mathematics and Economics", No. 44.
• Nelsen R.B. (1999): An Introduction to Copulas. Springer, New York.
• Ostasiewicz W. (red.), (2000): Modele aktuarialne. Wydawnictwo Akademii Ekonomicznej, Wrocław.
• Rolski T., Schmidli H., Schmidt V, Teugels J. (1999): Stochastic Process for Insurance and Finance. Wiley, New York.
• Shiu E. (1989): The Probability of Eventual Ruin in the Compound Binomial Model. "ASTIN Bulletin", No. 19.