The Exit Time And The Dividend Problem For Compound Poisson Risk Model

International Journal of Mathematics Trends and Technology (IJMTT)
© 2021 by IJMTT Journal
Volume-67 Issue-2
Year of Publication : 2021
Authors : Peng Li


MLA Style: Peng Li. "The Exit Time And The Dividend Problem For Compound Poisson Risk Model" International Journal of Mathematics Trends and Technology 67.2 (2021):57-67. 

APA Style: Peng Li(2021). The Exit Time And The Dividend Problem For Compound Poisson Risk Model. International Journal of Mathematics Trends and Technology, 57-67.

In this paper, we consider the classical risk model with mixed dividend strategy. Integro-differential equations for the Laplace transform of exit times from interval are derived. Unlike previous studies, this paper uses exit time to calculate the expected discounted dividend payments prior to ruin under compound Poisson model. When the claims are exponentially distributed, the analytical solution is presented.


[1] Fatmir Hoxha, Metoda të analizës numerike, Infbotues, Tiranë, 2008.
[2] Трпеновски Б., Целакоски Н., Елементи од нумеричката математика, Просветно Дело, Скопје, 1992.
[3] Chakrabarty, Dhritikesh. (2017). Backward Divided Difference: Representation of Numerical Data by a Polynomial Curve. 2. 1 – 6.
[4] Wolfram Mathematica, link: [online accessed on 06.01.2020].
[5] Key Indicators from theme: Education and Science, State Statistical Office, link: [online accessed on 25.06.2019]
[6] Richard L. Burden, J. Douglas Faires, Numerical Analysis, Brooks Cole Pub., 2011.
[7] Stojanovska L. Trifunov Z. (2010) „Constructing and Exploring Triangles with GeoGebra“. Anale Seria Informatica, Vol VIII, Fac.2, România, pp. 45-54.
[8] Trifunov Z., Karamazova E., … (2015) „Introduction of discrete and continuous random variable“. LAP LAMBERT Academic Publishing. ISBN: 978-3-659-79405-6
[9] Biswajit Das, Dhritikesh Chakrabarty (2016) „ Newton’s backward interpolation: Representation of numerical data by a polynomial curve“, International Journal of Applied Research 2016; 2(10): 513-517, pp 513-517.
[10] Robert J Schilling, Sandra L Harries. „Applied Numerical Methods for Engineers“, Brooks /Cole, Pacific Grove, CA, 2000
[11] A. Favieri, (2018), „Hypertext on laplace transform using wolfram mathematica“, INTED2018 Proceedings, ISBN: 978-84-697-9480-7, ISSN: 2340-1079, pp. 4979-4986

Keywords : Classical risk model, Mixed dividend strategy, Dividend payment, Exponential claims, Exit times