Advances in Applied Probability

The optimal dividend problem in the dual model

Erik Ekström and Bing Lu

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We study de Finetti's optimal dividend problem, also known as the optimal harvesting problem, in the dual model. In this model, the firm value is affected both by continuous fluctuations and by upward directed jumps. We use a fixed point method to show that the solution of the optimal dividend problem with jumps can be obtained as the limit of a sequence of stochastic control problems for a diffusion. In each problem, the optimal dividend strategy is of barrier type, and the rate of convergence of the barrier and the corresponding value function is exponential.

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Adv. in Appl. Probab. Volume 46, Number 3 (2014), 746-765.

First available in Project Euclid: 29 August 2014

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Zentralblatt MATH identifier

Primary: 93E20: Optimal stochastic control
Secondary: 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems) 60G51: Processes with independent increments; Lévy processes

Optimal distribution of dividends de Finetti's dividend problem optimal harvesting singular stochastic control jump diffusion model


Ekström, Erik; Lu, Bing. The optimal dividend problem in the dual model. Adv. in Appl. Probab. 46 (2014), no. 3, 746--765. doi:10.1239/aap/1409319558.

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  • Alvarez, L. H. R. and Rakkolainen, T. A. (2009). Optimal payout policy in presence of downside risk. Math. Meth. Operat. Res. 69, 27–58.
  • Asmussen, S. and Taksar, M. (1997). Controlled diffusion models for optimal dividend pay-out. Insurance Math. Econom. 20, 1–15.
  • Avanzi, B., Gerber, H. U. and Shiu, E. S. W. (2007). Optimal dividends in the dual model. Insurance Math. Econom. 41, 111–123.
  • Avanzi, B., Shen, J. and Wong, B. (2011). Optimal dividends and capital injections in the dual model with diffusion. ASTIN Bull. 41, 611–644.
  • Avram, F., Palmowski, Z. and Pistorius, M. R. (2007). On the optimal dividend problem for a spectrally negative Lévy process. Ann. Appl. Prob. 17, 156–180.
  • Bayraktar, E. and Egami, M. (2008). Optimizing venture capital investments in a jump diffusion model. Math. Meth. Operat. Res. 67, 21–42.
  • Bayraktar, E. and Xing, H. (2009). Pricing American options for jump diffusions by iterating optimal stopping problems for diffusions. Math. Meth. Operat. Res. 70, 505–525.
  • Bayraktar, E., Kyprianou, A. E. and Yamazaki, K. (2013). On optimal dividends in the dual model. ASTIN Bull. 43, 359–372.
  • Dai, H., Liu, Z. and Luan, N. (2010). Optimal dividend strategies in a dual model with capital injections. Math. Meth. Operat. Res. 72, 129–143.
  • Davis, M. H. A. (1993). Markov Models and Optimization (Monogr. Statist. Appl. Prob. 49). Chapman & Hall, London.
  • Dayanik, S., Poor, H. V. and Sezer, S. O. (2008). Multisource Bayesian sequential change detection. Ann. Appl. Prob. 18, 552–590.
  • Gugerli, U. S. (1986). Optimal stopping of a piecewise-deterministic Markov process. Stochastics 19, 221–236.
  • Loeffen, R. L. (2008). On optimality of the barrier strategy in de Finetti's dividend problem for spectrally negative Lévy processes. Ann. Appl. Prob. 18, 1669–1680.
  • Loeffen, R. L. and Renaud, J.-F. (2010). De Finetti's optimal dividends problem with an affine penalty function at ruin. Insurance Math. Econom. 46, 98–108.
  • Zhanblan-Pike, M. and Shiryaev, A. N. (1995). Optimization of the flow of dividends. Russian Math. Surveys 50, 257–277.