Discrete Time Markov Reward Processes a Motor Car Insurance Example


In this paper, a full treatment of homogeneous discrete time Markov reward processes is presented. The higher order moments of the homogeneous reward process are determined. In the last part of the paper, an application to the bonus-malus car insurance is presented. The application was constructed using real data.

Share and Cite:

G. Amico, J. Janssen and R. Manca, "Discrete Time Markov Reward Processes a Motor Car Insurance Example," Technology and Investment, Vol. 1 No. 2, 2010, pp. 135-142. doi: 10.4236/ti.2010.12016.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Howard R, “Dynamic Probabilistic Systems,” Vol. 1-2, Wiley, New York, 1971.
[2] R. Norberg, “Differential Equations for Moments of Pre-sent Values in Life Insurance,” Insurance: Mathematics and Economics, Vol. 17, No. 2, 1995, pp.171-180.
[3] J. Janssen and R. Manca, “Applied Semi-Markov Proc-esses,” Springer, New York, 2006.
[4] F. Stenberg, R. Manca and D. Silvestrov, “An Algorithmic Approach to Discrete Time Non-Homogeneous Backward Semi-Markov Reward Processes with an Application to Disability Insurance,” Methodology and Computing in Applied Probability, Vol. 9, No. 4, 2007, pp. 497-519.
[5] J. Janssen and R. Manca, “Semi-Markov Risk Models for Finance, Insurance and Reliability,” Springer, New York. 2007.
[6] J. Janssen, R. Manca and di P. E. Volpe, “Mathematical Finance: Deterministic and Stochastic Models,” STE and Wiley, London, 2008.
[7] S. G. Kellison, “The Theory of Interest,” 2nd Edition, Homewood, Irwin, 1991.
[8] M. A. Qureshi and H. W. Sanders, “Reward Model Solu-tion Methods with Impulse and Rate Rewards: An Algo-rithmic and Numerical Results,” Performance Evaluation, Vol. 20, No. 4, 1994, pp. 413-436.
[9] J. M. Hoem, “The Versatility of the Markov Chain as a Tool in the Mathematics of Life Insurance,” Transactions of the 23rd International Congress of Actuaries, Vol. 3, 1988, pp. 171-202.
[10] H. Wolthuis, “Life Insurance Mathematics (the Markovian Model),” 2nd Edition, Peeters Publishers, Herent. 14, 2003.
[11] E. Çinlar, “Markov Renewal Theory,” Advances in Applied Probability, Vol. 1, 1969, pp. 123-187.
[12] F. Stenberg, R. Manca and D. Silvestrov, “Semi-Markov Reward Models for Disability Insurance,” Theory of Stochastic Processes, Vol. 12, No. 28, 2006, pp. 239-254.
[13] J. Lemaire, “Bonus-Malus Systems in Automobile Insur-ance,” Kluwer Academic Publisher, Boston, 1995.
[14] B. Sundt, “An Introduction to Non Life Insurance Mathe-matics,” Veroffentlichungen des Istitute fur Versich-erun gswissenschaft der Universitat Mannheim, 3rd Edition, 1993.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.