Optimal double stopping time (0909.3363v1)

Abstract: We consider the optimal double stopping time problem defined for each stopping time $S$ by $v(S)=\esssup{E[ψ(τ_1, τ_2) | \F_S], τ_1, τ_2 \geq S }$. 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 {\em new reward} $φ$ such that the value function $v(S)$ satisfies $v(S)=\esssup{E[φ(τ) | \F_S], τ\geq S }$. Finally, we give an example of an american option with double exercise time.