Consider an investor who is holding one share of a stock whose price is evolving according...

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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)+oW(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) +A where A > 0. 1. (10 points) What is the cumulative distribution function of the hitting time TS(0)+A? 2. (10 points) Give also the density of the distribution of the hitting time TS(0)+A 3. (10 points) What is the distribution of the hitting time TS(0)-8, 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)+oW(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) +A where A > 0. 1. (10 points) What is the cumulative distribution function of the hitting time TS(0)+A? 2. (10 points) Give also the density of the distribution of the hitting time TS(0)+A 3. (10 points) What is the distribution of the hitting time TS(0)-8, 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)?

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1 10 points The cumulative distribution function CDF of the hitting time S0 which is t... View the full answer