Consider an investor who is holding one share of a stock whose price is evolving according to a standard Brownian motion process, i.e. S(u)=S(0)+W(u),u0, where >0 is the volatility coefficient. This investor purchased the stock at a price S(0)>0 at time 0 and decides to sell the stock if it reaches the price S(0)+ where >0. 1. (5 points) What is the cumulative distribution function of the hitting time S(0)+ ? 2. (5 points) Give also the density of the distribution of the hitting time S(0)+. 3. (5 points) What is the distribution of the hitting time S(0), i.e. of the first time at which the asset price falls below S(0) where >0 is a positive constant smaller than S(0) ? Consider an investor who is holding one share of a stock whose price is evolving according to a standard Brownian motion process, i.e. S(u)=S(0)+W(u),u0, where >0 is the volatility coefficient. This investor purchased the stock at a price S(0)>0 at time 0 and decides to sell the stock if it reaches the price S(0)+ where >0. 1. (5 points) What is the cumulative distribution function of the hitting time S(0)+ ? 2. (5 points) Give also the density of the distribution of the hitting time S(0)+. 3. (5 points) What is the distribution of the hitting time S(0), i.e. of the first time at which the asset price falls below S(0) where >0 is a positive constant smaller than S(0)