TY - JOUR
T1 - Characterization of stochastic control with optimal stopping in a Sobolev space
AU - Chen, Xiaoshan
AU - Song, Qingshuo
AU - Yi, Fahuai
AU - Yin, George
PY - 2013/6
Y1 - 2013/6
N2 - This work develops a new framework for a class of stochastic control problems with optimal stopping. One of our main motivations stems from dealing with the option pricing of American type. The value function is characterized as the unique solution of a partial differential equation in a Sobolev space. Together with certain regularities and estimates of the value function, the existence of the optimal strategy is established. The key ingredient is the use of the Itô formula for functions in a Sobolev space. Our approach provides a new alternative method for dealing with a class of stochastic control problems. © 2013 Elsevier Ltd. All rights reserved.
AB - This work develops a new framework for a class of stochastic control problems with optimal stopping. One of our main motivations stems from dealing with the option pricing of American type. The value function is characterized as the unique solution of a partial differential equation in a Sobolev space. Together with certain regularities and estimates of the value function, the existence of the optimal strategy is established. The key ingredient is the use of the Itô formula for functions in a Sobolev space. Our approach provides a new alternative method for dealing with a class of stochastic control problems. © 2013 Elsevier Ltd. All rights reserved.
KW - Generalized Itô formula
KW - Optimal stopping
KW - Stochastic control
KW - Weak verification theorem
UR - http://www.scopus.com/inward/record.url?scp=84877582802&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84877582802&origin=recordpage
U2 - 10.1016/j.automatica.2013.02.040
DO - 10.1016/j.automatica.2013.02.040
M3 - RGC 21 - Publication in refereed journal
SN - 0005-1098
VL - 49
SP - 1654
EP - 1662
JO - Automatica
JF - Automatica
IS - 6
ER -