Commenced in January 2007
Paper Count: 32009
A Hyperexponential Approximation to Finite-Time and Infinite-Time Ruin Probabilities of Compound Poisson Processes
Authors: Amir T. Payandeh Najafabadi
Abstract:This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equation). Application of our findings has been given through a simulation study.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1339712Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1058
 Albrecher, H., Teugels, J. L., & Tichy, R. F. (2001). On a gamma series expansion for the time-dependent probability of collective ruin. Insurance: Mathematics and Economics, 29(3), 345–355.
 Avram, F., Chedom, D. F., & Horváth, A. (2011). On moments based Padé approximations of ruin probabilities. Journal of computational and applied mathematics, 235(10), 3215–3228.
 Asmussen, S., & Albrecher, H. (2010). Ruin probabilities (Vol. 14). World Scientific, New Jersey.
 Belding, D. F., & Mitchell, K. J. (2008). Foundations of analysis (Vol. 79). Courier Corporation, New York.
 Bilik, A. (2008). Heavy-tail central limit theorem. Lecture notes from University of California, San Diego.
 Champeney, D. C. (1987). A handbook of Fourier theorems. Cambridge University press, New York.
 Feldmann, A., & Whitt, W. (1998). Fitting mixtures of exponentials to long–tail distributions to analyze network performance models. Performance evaluation, 31(3-4), 245–279.
 Feller, W. (1971). An introduction to probability and its applications, Vol. II. Wiley, New York.
 Jewell, N. P. (1982). Mixtures of Exponential Distributions. The Annals of Statistics, 10(2), 479–484.
 Kaas, R., Goovaerts, M., Dhaene, J., & Denuit, M. (2008). Modern actuarial risk theory: using R (Vol. 128). Springer-Verlag, Berlin Heidelberg.
 Kucerovsky, D., & Payandeh Najafabadi, A. T. (2009). An approximation for a subclass of the Riemann-Hilbert problems. IMA journal of applied mathematics, 74(4), 533–547.
 Kucerovsky, D. Z. & Payandeh Najafabadi, A. T. (2015). Solving an integral equation arising from the Ruin probability of long-term Bonus–Malus systems. Preprinted.
 Lukacs, E. (1987). Characteristic Functions. Oxford University Press, New York.
 Makroglou, A. (2003). Integral equations and actuarial risk management: some models and numerics. Mathematical Modelling and Analysis, 8(2), 143–154.
 Melnikov, A. (2011). Risk analysis in finance and insurance. CRC Press.
 Merzon, A., & Sadov, S. (2011). Hausdorff-Young type theorems for the Laplace transform restricted to a ray or to a curve in the complex plane. arXiv preprint arXiv:1109.6085.
 Pandey, J. (1996). The Hilbert transform of Schwartz distributions and application. John Wiley & Sons, New York.
 Pervozvansky, A. A. (1998). Equation for survival probability in a finite time interval in case of non-zero real interest force. Insurance: Mathematics and Economics, 23(3), 287–295.
 Qin, L., & Pitts, S. M. (2012). Nonparametric estimation of the finite-time survival probability with zero initial capital in the classical risk model. Methodology and Computing in Applied Probability, 14(4), 919-936.
 Rachev, S. T. (Ed.). (2003). Handbook of Heavy Tailed Distributions in Finance: Handbooks in Finance (Vol. 1). Elsevier, Netherlands.
 Sadov, S. Y. (2013). Characterization of Carleson measures by the Hausdorff-Young property. Mathematical Notes, 94(3-4), 551-558.
 Schmidli, H (2006). Lecture notes on Risk Theory. Institute of Mathematics University of Cologne, German.
 Sylvia, F. S. (2008). Finite mixture and Markov switching models: Implementation in MATLAB using the package bayesf Version 2.0. Springer-Verlag, New York.
 Tran, D. X. (2015). Padé approximants for finite time ruin probabilities. Journal of Computational and Applied Mathematics, 278, 130-137.
 Walnut, D. F. (2002). An introduction to wavelet analysis. 2nd ed. Birkhäuser publisher, New York.