Optimal double stopping time problem

Abstract

We consider the optimal double stopping time problem v ( S ) = ess sup { E [ ψ ( τ 1 , τ 2 ) | F S ] , τ 1 , τ 2 ⩾ S } for each stopping time S. Following the optimal one stopping time problem, we study the existence of optimal stopping times and give a method to compute them. The key point is the construction of a new reward ϕ such that v ( S ) = ess sup { E [ ϕ ( τ ) | F S ] , τ ⩾ S } .