# ON OPTIMAL DIVIDENDS IN THE DUAL MODEL

@article{Bayraktar2013ONOD, title={ON OPTIMAL DIVIDENDS IN THE DUAL MODEL}, author={Erhan Bayraktar and Andreas E. Kyprianou and Kazutoshi Yamazaki}, journal={ASTIN Bulletin}, year={2013}, volume={43}, pages={359 - 372} }

Abstract We revisit the dividend payment problem in the dual model of Avanzi et al. ([2–4]). Using the fluctuation theory of spectrally positive Lévy processes, we give a short exposition in which we show the optimality of barrier strategies for all such Lévy processes. Moreover, we characterize the optimal barrier using the functional inverse of a scale function. We also consider the capital injection problem of [4] and show that its value function has a very similar form to the one in which…

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## References

SHOWING 1-10 OF 21 REFERENCES

### Optimal Dividends in the Dual Model with Diffusion

- Mathematics
- 2008

In the dual model, the surplus of a company is a Levy process with sample paths that are skip-free downwards. In this paper, the aggregate gains process is the sum of a shifted compound Poisson…

### On optimality of the barrier strategy in de Finetti’s dividend problem for spectrally negative Lévy processes

- Mathematics
- 2008

We consider the classical optimal dividend control problem which was proposed by de Finetti [Trans. XVth Internat. Congress Actuaries 2 (1957) 433-443]. Recently Avram, Palmowski and Pistorius [Ann.…

### On the optimal dividend problem for a spectrally negative Lévy process

- Mathematics, Business
- 2007

In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative L\'{e}vy process in the absence of dividend payments. The classical…

### A note on scale functions and the time value of ruin for Levy insurance risk processes

- Mathematics
- 2010

### Optimal Dividends and Capital Injections in the Dual Model with Diffusion

- Business
- 2010

The dual model with diffusion is appropriate for companies with continuous expenses that are offset by stochastic and irregular gains. Examples include research-based or commission-based companies.…

### OPTIMAL REINSURANCE AND DIVIDEND DISTRIBUTION POLICIES IN THE CRAMÉR‐LUNDBERG MODEL

- Mathematics, Economics
- 2005

We consider that the reserve of an insurance company follows a Cramér‐Lundberg process. The management has the possibility of controlling the risk by means of reinsurance. Our aim is to find a…

### Optimizing venture capital investments in a jump diffusion model

- BusinessMath. Methods Oper. Res.
- 2008

Two practical optimization problems in relation to venture capital investments and/or Research and Development (R&D) investments, concerned with optimal dividend policy and optimal control policy are studied.

### Special, conjugate and complete scale functions for spectrally negative Lévy processes

- Mathematics
- 2007

Following from recent developments in Hubalek and Kyprianou [28], the objective of this paper is to provide further methods for constructing new families of scale functions for spectrally negative…

### Introductory Lectures on Fluctuations of Lévy Processes with Applications

- Mathematics
- 2006

Levy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their mathematical significance…