A share of a company's stock is currently traded at Xo = 50 Gils. Its price...

 

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A share of a company's stock is currently traded at Xo = 50 Gils. Its price is assumed to follow an arithmetic Brownian motion with drift coefficient μ = 5 Gils.year ¹ and diffusion coefficient = 4 Gils.year −1/2, so that at any time t> 0 -1 o Xt = Xo+pt+oWt, where W is a (standard) Brownian motion. Give your answer with 2 decimal digits (e.g. 3.14). (a) What is the probability that the stock price will be less than or equal to U = 55 Gils in t = 4 years ? (b) What is the probability that the stock price will be greater than or equal to L 65 Gils in t = 3 3 years ? (c) Compute the expected wealth after t = 2 (d) Compute the standard deviation of the wealth after t = 2 years. years. A share of a company's stock is currently traded at Xo = 50 Gils. Its price is assumed to follow an arithmetic Brownian motion with drift coefficient μ = 5 Gils.year ¹ and diffusion coefficient = 4 Gils.year −1/2, so that at any time t> 0 -1 o Xt = Xo+pt+oWt, where W is a (standard) Brownian motion. Give your answer with 2 decimal digits (e.g. 3.14). (a) What is the probability that the stock price will be less than or equal to U = 55 Gils in t = 4 years ? (b) What is the probability that the stock price will be greater than or equal to L 65 Gils in t = 3 3 years ? (c) Compute the expected wealth after t = 2 (d) Compute the standard deviation of the wealth after t = 2 years. years.

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To solve the given problem we will use the formulas and properties of arithmetic Brownian motion a T... View the full answer