Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-30T03:52:38.541Z Has data issue: false hasContentIssue false
  • English
  • Français

Ruin Theory in a Discrete Time Risk Model with Interest Income

Published online by Cambridge University Press:  10 June 2011

L. Sun  and
H. Yang
L. Sun
Affiliation:
Department of Mathematics, Fudan University, Shanghai 200433, P. R. China., Email: ljuan@fudan.edu.cn
H. Yang
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong., Tel: +852-2857-8322, Fax: +852-2858-9041, Email:hlyang@hkusua.hku.hk
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we consider a discrete time insurance risk model with interest income. Using the recursive calculation method of De Vylder & Goovaerts (1988), recursive equations for the finite time ruin probabilities and the distribution of the time of ruin are derived. Fredholm type integral equations for the ultimate ruin probability, the distribution of the severity of ruin, the joint distribution of surplus before and after ruin, and the probability of absolute ruin are obtained. Numerical results are included.

Keywords

Ruin ProbabilitySeverity of RuinAbsolute Ruin ProbabilityInterest IncomeRecursive CalculationFredholm Type Integral Equation
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 9 , Issue 3 , 01 August 2003 , pp. 637 - 652
Copyright
Copyright © Institute and Faculty of Actuaries 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cheng, S., Gerber, H.U. & Shiu, E.S.W. (2000). Discounted probabilities and ruin theory in the compound binomial model. Insurance: Mathematics and Economics, 26, 239–250.Google Scholar
Dassios, A. & Embrechts, P. (1989). Martingales and insurance risk. Commun. Statist. Stochastic Models, 5(2), 181–217.CrossRefGoogle Scholar
De Vylder, F. & Goovaerts, M.J. (1988). Recursive calculation of finite-time ruin probabilities. Insurance: Mathematics and Economics, 7, 1–7.Google Scholar
Delves, L.M. & Mohamed, J.L. (1985). Computational methods for integral equations. Cambridge University Press, Cambridge, U.K.CrossRefGoogle Scholar
Dickson, D.C.M. (1989). Recursive calculation of the probability and severity of ruin. Insurance: Mathematics and Economics, 8, 145–148.Google Scholar
Dickson, D.C.M. (1992). On the distribution of the surplus prior to ruin. Insurance: Mathematics and Economics, 11, 191–207.Google Scholar
Dickson, D.C.M. & Egidio dos Reis, A.D. (1994). Ruin problems and dual events. Insurance: Mathematics and Economics, 14, 51–60.Google Scholar
Dickson, D.C.M. & Waters, H.R. (1992). The probability and severity of ruin in finite and infinite time. Astin Bulletin, 22(2), 177–190.CrossRefGoogle Scholar
Dickson, D.C.M. & Waters, H.R. (1999). Ruin probabilities with compounding assets. Insurance: Mathematics and Economics, 25, 49–62.Google Scholar
Dufresne, F. & Gerber, H.U. (1988). The surpluses immediately before and at ruin, and the amount of the claim causing ruin. Insurance: Mathematics and Economics, 7, 193–199.Google Scholar
Egidio dos Reis, A.D. (2000). On the moments of ruin and recovery times. Insurance: Mathematics and Economics, 27, 331–343.Google Scholar
Gerber, H.U., Goovaerts, M.J. & Kaas, R. (1987). On the probability and severity of ruin. ASTIN Bulletin, 17, 151–163.CrossRefGoogle Scholar
Gerber, H.U. & Shiu, E.S.W. (1998). On the time value of ruin. North American Actuarial Journal, 2(1), 48–72.CrossRefGoogle Scholar
Gerber, H.U. & Shiu, E.S.W. (1997). The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. Insurance: Mathematics and Economics, 21, 129–137.Google Scholar
Li, S. & Garrido, J. (2002). On the time value of ruin in the discrete time risk model. Working paper 02–18, Business Economics Series 12, Departamento de Economia de la Empresa, Universidad Carlos III de Madrid, http://docubib.uc3m.es/WORKINGPAPERS/WB/wb021812.pdfGoogle Scholar
Lin, X.S. & Willmot, G.E. (2000). The moments of the time of ruin, the surplus before ruin, and the deficit at ruin. Insurance: Mathematics and Economics, 27, 19–44.Google Scholar
Panjer, H.H. & Willmot, G.E. (1992). Insurance risk loss models. Society of Actuaries, Schaumburg.Google Scholar
Willmot, G.E. (1996). A non-exponential generalization of an inequality arising in queueing and insurance risk. Journal of Applied Probability, 33, 176–183.CrossRefGoogle Scholar
Willmot, G.E. (2000). On evaluation of the conditional distribution of the deficit at the time of ruin. Scandinavian Actuarial Journal, 100(1), 63–79.CrossRefGoogle Scholar
Yang, H. (1999). Non-exponential bounds for ruin probability with interest effect included. Scandinavian Actuarial Journal, 1, 66–79.CrossRefGoogle Scholar