Application of asymptotic behaviour of distribution of maximum loss in stock prices

Maximum loss in the price of an asset is widely used as a measure of risk in financial markets. There are some analytical results on maximum loss of a Brownian motion, but for now such results do not exist for fractional Brownian motion. Since most work on maximum loss is empirical, it is relevant to work on finding and to improve new bounds related to this stochastic variable. In this thesis, we give some pre-existed results on the distribution and expected value of Brownian motion with application to finance and present a new improved theoretically proven lower bound to the expected value of maximum loss of fractional Brownian motion up to time 1. Later we generalize it up to any time t. Finally we perform a real data test to verify the results on the bounds of maximum loss of fractional Brownian motion.