Optimal stopping of oscillating Brownian motion

Mordecki, Ernesto - Salminen, Paavo

Resumen:

We solve optimal stopping problems for an oscillating Brownian motion, i.e. a diffusion with positive piecewise constant volatility changing at the point x=0. Let σ1 and σ 2 denote the volatilities on the negative and positive half-lines, respectively. Our main result is that continuation region of the optimal stopping problem with reward ((1+x)+)2 can be disconnected for some values of the discount rate when 2 σ 21 <σ22. Based on the fact that the skew Brownian motion in natural scale is an oscillating Brownian motion, the obtained results are translated into corresponding results for the skew Brownian motion.


Detalles Bibliográficos
2019
Excessive function
Integral representation of excessive functions
Inglés
Universidad de la República
COLIBRI
https://hdl.handle.net/20.500.12008/28109
Acceso abierto
Licencia Creative Commons Atribución (CC - By 4.0)