On non-trivial barrier solutions of the dividend problem for a diffusion under constant and proportional transaction costs

TY - JOUR

T1 - On non-trivial barrier solutions of the dividend problem for a diffusion under constant and proportional transaction costs

AU - Bai, Lihua

AU - Paulsen, Jostein

PY - 2012/12

Y1 - 2012/12

N2 - In Bai and Paulsen [L. Bai, J. Paulsen, Optimal dividend policies with transaction costs for a class of diffusion processes, SIAM J. Control Optim. 48 (2010) 4987-5008] the optimal dividend problem under transaction costs was analyzed for a rather general class of diffusion processes. It was divided into several subclasses, and for the majority of subclasses the optimal policy is a simple barrier policy; whenever the process hits an upper barrier u *, reduce it to u *-ξ through a dividend payment. After transaction costs, the shareholder receives kξ-K. It was proved that a simple barrier strategy is not always optimal, and here these more difficult cases are solved. The optimal solutions are rather complicated, but interesting.

AB - In Bai and Paulsen [L. Bai, J. Paulsen, Optimal dividend policies with transaction costs for a class of diffusion processes, SIAM J. Control Optim. 48 (2010) 4987-5008] the optimal dividend problem under transaction costs was analyzed for a rather general class of diffusion processes. It was divided into several subclasses, and for the majority of subclasses the optimal policy is a simple barrier policy; whenever the process hits an upper barrier u *, reduce it to u *-ξ through a dividend payment. After transaction costs, the shareholder receives kξ-K. It was proved that a simple barrier strategy is not always optimal, and here these more difficult cases are solved. The optimal solutions are rather complicated, but interesting.

M3 - Journal article

SN - 0304-4149

VL - 122

SP - 4005

EP - 4027

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

ER -