TY - JOUR

T1 - Discussion on “An effective method for the explicit solution of sequential problems on the real line” by Sören Christensen

AU - Buonaguidi, Bruno

PY - 2017

Y1 - 2017

N2 - 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].

AB - 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].

KW - Free-boundary problem

KW - Modeling and Simulation

KW - Statistics and Probability

KW - geometric Brownian motion

KW - optimal stopping

KW - perpetual American put option

KW - Free-boundary problem

KW - Modeling and Simulation

KW - Statistics and Probability

KW - geometric Brownian motion

KW - optimal stopping

KW - perpetual American put option

UR - http://hdl.handle.net/10807/133220

UR - http://www.tandf.co.uk/journals/titles/07474946.asp

U2 - 10.1080/07474946.2016.1275317

DO - 10.1080/07474946.2016.1275317

M3 - Article

SN - 0747-4946

VL - 36

SP - 24

EP - 26

JO - Sequential Analysis

JF - Sequential Analysis

ER -