Abstract
In recent years, insurance risk models with dividend payments have been studied extensively. The threshold dividend strategy assumes that dividends are paid out at the maximal admissible rate whenever the surplus exceeds a certain threshold. In this paper, we consider the classical risk model with constant interest under the threshold strategy. We derive integro-differential equations for the expected discounted penalty function. In some special cases with exponential claims, we are able to obtain closed-form expressions for the expected discounted penalty function.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
DE FINETTI, B. (1957): Su un’ impostazione alternativa dell teoria collettiva del rischio. Transactions of the XVth International Congress of Actuaries 2, 433-443.
FANG, Y. and WU, R. (2007): Optimal Dividend strategy in the Compound Poisson Model with constant interest. Stochastic Model 23, 149-166.
GERBER, H.U. and SHIU, E.S.W. (1998): On the time value of ruin. North American Actuarial Journal 2(1), 48-78.
GERBER, H.U. and SHIU, E.S.W. (2006): On optimal dividend strategies in the compound Poisson model. North American Actuarial Journal 10(2), 76-93.
LIN X.S. and PAVLOVA, K.P. (2006): The compound Poisson risk model with a threshold dividend strategy. Insurance: Mathematics and Economics 38, 57-80.
SLATER, L.J. (1960): Confluent Hypergeometric Functions. Cambridge University Press, London.
YUEN, K.C. and WANG, G. (2005). Some ruin problems for a risk process with stochastic interest. North American Actuarial Journal 9(3), 129-142.
YUEN, K.C., LU, Y. and WU, R. (2008a): The compound Poisson process perturbed by diffusion with a threshold dividend strategy. Applied Stochastic Models in Business and Industry, to appear.
YUEN, K.C., WANG, G. and LI, W.K. (2007): The Gerber-Shiu expected discounted penalty function for risk processes with interest and a constant dividend barrier. Insurance: Mathematics and Economics 40, 107-112.
YUEN, K.C., ZHOU, M. and GUO, J. (2008b): On a risk model with debit interest and dividend payments. Statistics and Probability Letters, to appear.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Physica-Verlag Heidelberg
About this paper
Cite this paper
Dong, Y., Yuen, K.C. (2008). The Classical Risk Model with Constant Interest and Threshold Strategy. In: Brito, P. (eds) COMPSTAT 2008. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2084-3_19
Download citation
DOI: https://doi.org/10.1007/978-3-7908-2084-3_19
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-2083-6
Online ISBN: 978-3-7908-2084-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)