Optimal Policies for Payment of Dividends through a Fixed Barrier at Discrete Time

Raúl Montes-de-Oca, Patricia Saavedra, Gabriel Zacarías-Espinoza, Daniel Cruz-Suárez

2017

Abstract

In this paper a discrete-time reserve process with a fixed barrier is presented and modelled as a discounted Markov Decision Process. The non-payment of dividends is penalized. The minimization of this penalty results in an optimal control problem. This work focuses on determining the sequence of premiums that minimize penalty costs, and obtaining a rate for the probability of ruin to ensure a sustainable reserve operation.

References

  1. Ash, R. B. and Doléans-Dade, C. (2000). Probability and Measure Theory. Elsevier, London, 2nd edition.
  2. Asmussen, S. (2010). Ruin Probability. World Scientific, Singapore, 2nd edition.
  3. Azcue, P. and Muler, N. (2014). Stochastic Optimization in Insurance a Dynamic Programming Approach. Springer, London.
  4. Breiman, L. (1992). Probability. SIAM, Berkeley.
  5. Bulinskaya, Y. G. and Muromskaya, A. (2014). Discretetime insurance model with capital injections and reinsurance. Methodol. Comput. Appl. Probab.
  6. Bäuerle, N. and Rieder, U. (2011). Markov Decision Processes with Applications to Finance. Springer, Berlin.
  7. Cramér, H. (1930). On the Mathematical Theory of Risk. Skandia Jubillee Volume, Stockholm.
  8. Cruz-Suárez, D., de Oca, R. M., and Salem-Silva, F. (2004). Conditions for the uniqueness of optimal policies of discounted markov decision processes. Math. Methods Oper. Res., 60:415-436.
  9. De-Finetti, B. (1957). Su un'impostaziones alternativa della teoria collectiva del rischio. Trans. XV. Int. Congr. Act., 2:433-443.
  10. Diasparra, M. A. and Romera, R. (2009). Bounds for the ruin probability of a discrete-time risk process. J. Appl. Probab., 46:99-112.
  11. Dickson, D. C. M. (2005). Insurance Risk and Ruin. Cambridge University Press, Cambridge.
  12. Dickson, D. C. M. and Waters, H. R. (2004). Some optimal dividend problems. ASTIN Bull., 34:49-74.
  13. Finch, P. D. (1960). Deterministic costumer impatience in the queueing system gi/m/1. Biometrika, 47:45-52.
  14. Gerber, H. U. (1981). On the probability of ruin in the presence of a linear dividend barrier. Scand. Acutarial J., pages 105-115.
  15. Gerber, H. U., Shiu, E. S. W., and Smith, N. (2006). Maximizing dividends without bankruptcy. ASTIN Bull., 36:5-23.
  16. Ghosal, A. (1970). Some Aspects od Queueing and Storage System. Springer Verlag, New York.
  17. Hernández-Lerma, O. and Lasserre, J. B. (1996). Discretetime Markov Control Processes: Basic Optimality Criteria. Springer Verlag, New York.
  18. Li, S., Lu, Y., and Garrido, J. A. (2009). A review of discrete-time risk models. Rev. R. Acad. Cien. Serie A. Mat., 103(2):321-337.
  19. Lindvall, T. (1992). Lectures on the Coupling Method. Wiley, New York.
  20. Lundberg, F. (1909). Über die theorie der ruckversicherung. Transactions of the VIth International Congress of Actuaries, 1:877-948.
  21. Martin-Löf, A. (1994). Lectures on the use of control theory in insurance. Scand. Actuarial J., pages 1-25.
  22. Martínez-Morales, M. (1991). Adaptive Premium in an Insurance Risk Process, Doctoral Thesis. Texas Tech University, Texas.
  23. Rolski, T., Schmidli, H., Schmidt, V., and Teugels, J. L. (1999). Stochastic Processes for Insurance and Finance. Wiley, Chichester.
  24. Royden, H. L. (1988). Real Analysis. Macmillan, New York.
  25. Schmidli, H. (2009). Stochastic Control in Insurance. Springer, London.
  26. Schäl, M. (2004). On discrete-time dynamic programming in insurance: Exponential utility and minimizing the ruin probability. Scand. Actuarial J., pages 189-210.
  27. Wilks, D. S. (2011). Statistical Methods in the Atmospheric Sciences. Academic Press, Burlington.
Download


Paper Citation


in Harvard Style

Montes-de-Oca R., Saavedra P., Zacarías-Espinoza G. and Cruz-Suárez D. (2017). Optimal Policies for Payment of Dividends through a Fixed Barrier at Discrete Time . In Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-218-9, pages 140-149. DOI: 10.5220/0006193701400149


in Bibtex Style

@conference{icores17,
author={Raúl Montes-de-Oca and Patricia Saavedra and Gabriel Zacarías-Espinoza and Daniel Cruz-Suárez},
title={Optimal Policies for Payment of Dividends through a Fixed Barrier at Discrete Time},
booktitle={Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2017},
pages={140-149},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006193701400149},
isbn={978-989-758-218-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - Optimal Policies for Payment of Dividends through a Fixed Barrier at Discrete Time
SN - 978-989-758-218-9
AU - Montes-de-Oca R.
AU - Saavedra P.
AU - Zacarías-Espinoza G.
AU - Cruz-Suárez D.
PY - 2017
SP - 140
EP - 149
DO - 10.5220/0006193701400149