# A Stochastic Control Problem with Linearly Bounded Control Rates in a Brownian Model

@article{Renaud2021ASC, title={A Stochastic Control Problem with Linearly Bounded Control Rates in a Brownian Model}, author={Jean-François Renaud and Clarence Simard}, journal={SIAM J. Control. Optim.}, year={2021}, volume={59}, pages={3103-3117} }

Aiming for more realistic optimal dividend policies, we consider a stochastic control problem with linearly bounded control rates using a performance function given by the expected present value of dividend payments made up to ruin. In a Brownian model, we prove the optimality of a member of a new family of control strategies called delayed linear control strategies, for which the controlled process is a refracted diffusion process. For some parameters specifications, we retrieve the strategy…

## One Citation

De Finetti's control problem with a concave bound on the control rate

- Mathematics
- 2022

. We consider De Finetti’s control problem for absolutely continuous strategies with control rates bounded by a concave function and prove that a generalized mean-reverting strategy is optimal. In…

## References

SHOWING 1-10 OF 12 REFERENCES

On a Mean Reverting Dividend Strategy with Brownian Motion

- Business
- 2009

In actuarial risk theory, the introduction of dividend pay-outs in surplus models goes back to de Finetti (1957). Dividend strategies that can be found in the literature often yield pay-out patterns…

Risk Theory with Affine Dividend Payment Strategies

- Mathematics
- 2017

We consider a classical compound Poisson risk model with affine dividend payments. We illustrate how both by analytical and probabilistic techniques closed-form expressions for the expected…

Optimal Dividends

- Mathematics
- 2004

Abstract In the absence of dividends, the surplus of a company is modeled by a Wiener process (or Brownian motion) with positive drift. Now dividends are paid according to a barrier strategy:…

Fluctuations of Lévy Processes with Applications: Introductory Lectures

- Mathematics
- 2014

Levy Processes and Applications.- The Levy-Ito Decomposition and Path Structure.- More Distributional and Path-Related Properties.- General Storage Models and Paths of Bounded Variation.-…

Optimal dividend payouts for diffusions with solvency constraints

- BusinessFinance Stochastics
- 2003

A company where surplus follows a diffusion process and whose objective is to maximize expected discounted dividend payouts to the shareholders is considered, and it is shown theoretically how b0 can be calculated using this method, and examples are given for two special cases.

Representations of the First Hitting Time Density of an Ornstein-Uhlenbeck Process

- Mathematics
- 2005

ABSTRACT Three expressions are provided for the first hitting time density of an Ornstein-Uhlenbeck process to reach a fixed level. The first hinges on an eigenvalue expansion involving zeros of the…

Handbook of Brownian Motion - Facts and Formulae

- Mathematics
- 1996

I: Theory.- I. Stochastic processes in general.- II. Linear diffusions.- III. Stochastic calculus.- IV. Brownian motion.- V. Local time as a Markov process.- VI. Differential systems associated to…

Brownian Motion and Stochastic Calculus

- Mathematics
- 1987

This chapter discusses Brownian motion, which is concerned with continuous, Square-Integrable Martingales, and the Stochastic Integration, which deals with the integration of continuous, local martingales into Markov processes.