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Imagine a game. An urn contains six marbles: three green and three red. You remove them from the urn one at a time, revealing their colors. When you pull out a green marble I pay you $1, but if it's red you must pay me $1. If you are required to remove all the marbles the game is not very exciting, because by the end we'll always be exactly even. But imagine that I am willing to change the rules so that you can stop removing marbles at any time. This game is certainly better for you because you can always stop and walk away with your winnings if you happen to be ahead at some point or, if you're never ahead, play to the end when you'll be even. There is a catch: I'm going to charge you for this rule change.

How much would you be willing to pay?

This is an example of an option: you have the option at any point to stop removing marbles and walk away with your winnings. Probability is key to valuing the option because the exchange of money depends on the random order of the colors. But there is more to it than that. You must figure out the best strategy for managing your option. Should you stop as soon as you're $1 ahead? Should you go for more? This makes it an interesting optimization problem. Click here for the answer.

Options and other "derivative securities" in the real world are naturally much harder to analyze. In finance, it might be the random fluctuations of a stock price that determines the value of an option. Or perhaps it is changes in the level of Treasury yields. Whatever the case, probability theory and optimization techniques are important tools. Differential equations also play an equally important role. They are used to model how an asset's value changes as time elapses and as other related asset values change.

In our program you will learn about these and other exciting and important tools. The curriculum includes courses in probability theory, stochastic processes, partial differential equations, optimization techniques, Monte Carlo methods, modeling techniques, data analysis - all with many applications in finance. Applications will include security valuation, risk measurement and management, hedging techniques, and portfolio optimization. In addition to theory, you will learn very practical computational techniques through hands on experience.

After all, it's getting the answer that counts!