The Supremum the Infimum Maximum Gain and Maximum Loss of Brownian Motion with Drift

Related to risk and to hedging investors would be interested insupremum, infimum, maximum gain and maximum loss. Price ofstock can be modeled using Brownian motion. Here, we presentthe marginal and joint distributions of supremum, infimum, maxi-mum gain and maximum loss of Brownian motion with drift 0. Asan extension, we provide calculations of correlations for Brownianmotion with drift. We give number of results related to distributionsover various time. We present numerical studies of Brownian mo-tion with drift and collect conjectures on relation between maximumgain and maximum loss