Read e-book online An Elementary Introduction to Mathematical Finance, Third PDF

By Sheldon M. Ross

ISBN-10: 0521192536

ISBN-13: 9780521192538

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5) > 10). 1 in the approximation model to the Brownian motion process of the preceding problem. 5) > 10). 2. Find (a) P(S(1) > S(0)); (b) P(S(2) > S(1) > S(0)); (c) P(S(3) < S(1) > S(0)). 4. 6 Let S(t), t ≥ 0 be a geometric Brownian motion process with drift parameter μ and volatility parameter σ . Assuming that S(0) = s, find Var(S(t)). 7 Let {X (t), t ≥ 0} be a Brownian motion process with drift parameter μ and variance parameter σ 2 . Assume that X (0) = 0, and let Ty be the first time that the process is equal to y.

R EF ER ENC E [1] Ross, S. M. (2010). A First Course in Probability, 8th ed. Englewood Cliffs, NJ: Prentice-Hall. 2. 1 Continuous Random Variables Whereas the possible values of the random variables considered in the previous chapter constituted sets of discrete values, there exist random variables whose set of possible values is instead a continuous region. These continuous random variables can take on any value within some interval. For example, such random variables as the time it takes to complete an assignment, or the weight of a randomly chosen individual, are usually considered to be continuous.

Suppose that an individual owns two such batteries, one of which is to be used as a spare to replace the other when it fails. (a) What is the probability that the total life of the batteries will exceed 760 hours? (b) What is the probability that the second battery will outlive the first by at least 25 hours? (c) What is the probability that the longer-lasting battery will outlive the other by at least 25 hours? 7 The time it takes to develop a photographic print is a random variable with mean 18 seconds and standard deviation 1 second.

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An Elementary Introduction to Mathematical Finance, Third Edition by Sheldon M. Ross


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