Discussion on “An effective method for the explicit solution of sequential problems on the real line” by Sören Christensen

Let X := (Xt)t≥0 be a geometric Brownian motion, ℙx be the probability measure under which X starts at x>0, and T be an exponential random variable independent of X. Using the very interesting results presented by Professor Christensen and exploiting the free-boundary problem solution for the optimal exercise of a perpetual American put option, we provide an alternative way to derive the well-known quantity Ex[inf0≤t≤TXt].