Consider the Bermudan option pricing problem, where the Bermudan option has d exercise opportunities at times t₁ 2 d = T , with t₁ ≥ 0. Here, the issue date and maturity date of the Bermudan option are taken to be 0 and T , respectively. Let M_t denote the value at time t of $1 invested in the riskless money market account at time 0. Let h_t denote the payoff from exercise at time t and τ^∗ be a stopping time taking values in {t₁,t₂, ··· ,t_d}. The value of the Bermudan option at time 0 is given by

Consider the quantity defined by (Andersen and Broadie, 2004) 

explain why Q_ti gives the value of a Bermudan option that is newly issued at time t_i. Is it the same as the value at t_i of a Bermudan option issued at time 0? If not, explain why?