homework3.pdf - IEOR E4707 Spring 2019 Homework 3 This...

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IEOR E4707, Spring 2019: Homework 3 February 27, 2019 This homework is due on Tuesday, March 5, 2019 . You should write up your own answers and understand everything you write. You can apply directly a result stated in the lecture notes unless you are asked to prove it. You must show ALL YOUR WORK in order to receive credit. ANSWERS WITHOUT APPROPRIATE JUSTIFICATION WILL RECEIVE NO CREDIT. Throughout this exercise a filtered probability space (Ω , F , P ; { F W t } t 0 ) is given in which is defined a one-dimensional Brownian motion W = { W t } t 0 . Moreover, T > 0 is fixed and given. Problem 1. The following is a map where nodes represent towns and the num- bers shown are the distances between two directly connected towns. Applying dynamic programming to find the shortest path from Town O to Town D, along with the corresponding shortest distance. Q Q Q Q Q Q P P P P P P P P P P P P P P P P P P Q Q Q Q Q Q S S S S S S S S Q Q Q Q Q Q P P P P P P O A B C E F G H I J D 3 2 5 3 6 4 5 6 3 5 4 5 2 5 3 7 3 6 Problem 2.

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