A company's cash position, measured in millions of dollars, and denoted by (X+) follows an arithme-...

  

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A company's cash position, measured in millions of dollars, and denoted by (X+) follows an arithme- tic Brownian motion with dynamics dXtadt +dWt along with the drift rate of a = 1.2 per annum and variance rate of 2 = 1.92 per annum. The initial cash position is Xo = 1. (a) What are the probability distributions of the cash position at the end of 1 month, 1 year and 3 years. (b) What are the probabilities of a negative cash position at the end of 1 month, 1 year and 3 years. A company's cash position, measured in millions of dollars, and denoted by (X+) follows an arithme- tic Brownian motion with dynamics dXtadt +dWt along with the drift rate of a = 1.2 per annum and variance rate of 2 = 1.92 per annum. The initial cash position is Xo = 1. (a) What are the probability distributions of the cash position at the end of 1 month, 1 year and 3 years. (b) What are the probabilities of a negative cash position at the end of 1 month, 1 year and 3 years.

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