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].
Buonaguidi, B., Discussion on “An effective method for the explicit solution of sequential problems on the real line” by Sören Christensen, <<SEQUENTIAL ANALYSIS>>, 2017; 36 (1): 24-26. [doi:10.1080/07474946.2016.1275317] [http://hdl.handle.net/10807/133220]
Discussion on “An effective method for the explicit solution of sequential problems on the real line” by Sören Christensen
Buonaguidi, Bruno
Primo
2017
Abstract
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].I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.