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On the Optimal Dividend Strategy in a Regime-Switching Diffusion Model

Part of: Stochastic analysis Mathematical economics Stochastic systems and control

Published online by Cambridge University Press:  04 January 2016

Jiaqin Wei ,
Rongming Wang  and
Hailiang Yang
Jiaqin Wei*
Affiliation:
East China Normal University
Rongming Wang*
Affiliation:
East China Normal University
Hailiang Yang*
Affiliation:
The University of Hong Kong
*
∗ Postal address: School of Finance and Statistics, East China Normal University, Shanghai, 200241, China.
∗ Postal address: School of Finance and Statistics, East China Normal University, Shanghai, 200241, China.
∗∗∗∗ Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China. Email address: [email protected]
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Abstract

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In this paper we consider the optimal dividend strategy under the diffusion model with regime switching. In contrast to the classical risk theory, the dividends can only be paid at the arrival times of a Poisson process. By solving an auxiliary optimal problem we show that the optimal strategy is the modulated barrier strategy. The value function can be obtained by iteration or by solving the system of differential equations. We also provide a numerical example to illustrate the effects of the restriction on the timing of the payment of dividends.

Keywords

Dividend strategyregime switchingHJB equationMarkov decision process

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 91B70: Stochastic models 60H30: Applications of stochastic analysis (to PDE, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 44 , Issue 3 , September 2012 , pp. 886 - 906
Copyright
© Applied Probability Trust 

References

Albrecher, H., Bäuerle, N. and Thonhauser, S. (2011). Optimal dividend-payout in random discrete time. Statist. Risk Modelling 28, 251–276 CrossRefGoogle Scholar
Albrecher, H., Cheung, E. C. K. and Thonhauser, S. (2011). Randomized observation periods for the compound poisson risk model: dividends. ASTIN Bull. 41, 645–672.Google Scholar
Albrecher, H., Gerber, H. U. and Shiu, E. S. W. (2011). The optimal dividend barrier in the gamma-omega model. Europ. Actuarial J. 1, 43–55.CrossRefGoogle Scholar
Bäuerle, N. and Rieder, U. (2011). Markov Decision Processes with Applications to Finance. Springer, Heidelberg.Google Scholar
Bayraktar, E. and Ludkovski, M. (2009). Sequential tracking of a hidden Markov chain using point process observations. Stoch. Process. Appl. 119, 1792–1822.Google Scholar
Davis, M. H. A. (1993). Markov Models and Optimization. Chapman & Hall, London.CrossRefGoogle Scholar
De Finetti, B. (1957). Su un'impostazione alternativa della teoria collecttiva del rischio. In Trans. 15th Internat. Congress of Actuaries, pp. 433–443.Google Scholar
Jiang, Z. and Pistorius, M. (2012). Optimal dividend distribution under Markov-regime switching. To appear in Finance Stoch. Google Scholar
Kyprianou, A. E. (2006). Introductory Lectures on Fluctuations of Lévy Processes with Applications. Springer, Berlin.Google Scholar
Polyanin, A. D. and Zaitsev, V. F. (1995). Handbook of Exact Solutions for Ordinary Differential Equations. CRC Press, Boca Raton, FL.Google Scholar
Sotomayor, L. R. and Cadenillas, A. (2011). Classical and singular stochastic control for the optimal dividend policy when there is regime switching. Insurance Math. Econom. 48, 344–354.CrossRefGoogle Scholar
Wang, H. (2001). Some control problems with random intervention times. Adv. Appl. Prob. 33, 404–422.Google Scholar
Wei, J. and Wang, R. (2012). A note on the optimal dividend strategies under the gamma-omega risk model. Submitted.Google Scholar
Wei, J., Yang, H. and Wang, R. (2011). Optimal threshold dividend strategies under the compound Poisson model with regime switching. In Stochastic Analysis with Financial Applications, eds Kohatsu-Higa, N. P. A. and Sheu, S., Birkhäser, Basel, pp. 413–429.Google Scholar