When x1 120 the two possible scenarios lead to a

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Unformatted text preview: rk in front of the (n + 1)th customer is that in front of the nth customer plus his service time, minus the time between the arrival of customers n and n + 1. If this is negative the server has caught up and the waiting time is 0. Suppose E ⇠< E ⌘i and let ✏ = (E ⌘i E ⇠i )/2. (a) Show that there is a K so that Ex (X1 x) ✏ for x K . (c) Let Uk = min{n : Xn K }. (b) Use the fact that XUk ^n + ✏(Uk ^ n) is a supermartingale to conclude that Ex Uk x/✏. 178 CHAPTER 5. MARTINGALES Chapter 6 Mathematical Finance 6.1 Two Simple Examples To warm up for the developments in the next section we will look at two simple concrete examples under the unrealistic assumption that the interest rate is 0. One period case. In our first scenario the stock is at 90 at time 0 and may be 80 or 120 at time 1. ⇠⇠ 90 XX ⇠⇠⇠ ⇠ 120 XXX X 80 Suppose now that you are o↵ered a European call option with strike price 100 and expiry 1. This means that after you see what happened to the stock, you have an option...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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