| Título: | On the Principle of Smooth Fit for Killed Diffusions |
| Autores: | Samee, Farman; University of Manchester |
| Fecha: | 2010-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Optimal stopping; discounted optimal stopping; principle of smooth fit; regular diffusion process; killed diffusion process; scale function; concave function Primary 60G40; Secondary 60J60 |
| Descripción: | We explore the principle of smooth fit in the case of the discounted optimal stopping problem $$ V(x)=\sup_\tau\, \mathsf{E}_x[e^{-\beta\tau}G(X_\tau)]. $$ We show that there exists a regular diffusion $X$ and differentiable gain function $G$ such that the value function $V$ above fails to satisfy the smooth fit condition $V'(b)=G'(b)$ at the optimal stopping point $b$. However, if the fundamental solutions $\psi$ and $\phi$ of the `killed' generator equation $L_X u(x) - \beta u(x) =0$ are differentiable at $b$ then the smooth fit condition $V'(b)=G'(b)$ holds (whenever $X$ is regular and $G$ is differentiable at $b$). We give an example showing that this can happen even when `smooth fit through scale' (in the sense of the discounted problem) fails. |
| Idioma: | No aplica |
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