论文信息 - Optimal stopping with irregular reward functions

Optimal stopping with irregular reward functions

We consider optimal stopping problems with finite horizon for one-dimensional diffusions. We assume that the reward function is bounded and Borel-measurable, and we prove that the value function is continuous and can be characterized as the unique solution of a variational inequality in the sense of distributions.

Damien Lamberton

[1] Timothy C. Johnson,et al. The solution to a second order linear ordinary differential equation with a non-homogeneous term that is a measure , 2007 .

[2] L. Stettner,et al. Stopping of functionals with discontinuity at the boundary of an open set , 2010, 1006.4283.

[3] N. U. Prabhu,et al. Stochastic Processes and Their Applications , 1999 .

[4] Xiongzhi Chen. Brownian Motion and Stochastic Calculus , 2008 .

[5] M. Yor,et al. Continuous martingales and Brownian motion , 1990 .

[6] Alain Bensoussan,et al. Applications of Variational Inequalities in Stochastic Control , 1982 .

[7] Bruno Bassan,et al. Optimal stopping problems with discontinous reward: Regularity of the value function and viscosity solutions , 2002 .

[8] Lepeltier,et al. A PROBABILISTIC APPROACH TO THE REDUITE IN OPTIMAL STOPPING , 2008 .