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Viewing: MATH 6442 : Stochastic Calculus Methods in Finance

Last approved: Mon, 10 Jul 2017 08:02:48 GMT

Last edit: Thu, 06 Jul 2017 18:47:23 GMT

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Columbian College of Arts and Sciences
Mathematics (MATH)
MATH
6442
Stochastic Calculus Methods in Finance
Stochastic Calculus in Finance
Fall 2017
3
Course Type
Lecture
Default Grading Method
Letter Grade

No
No
MATH 2184 and MATH 2233
Corequisites

20

Frequency of Offering

Term(s) Offered

Are there Course Equivalents?
No
 
No
Fee Type


No


Review of finance and probability theory. Brownian motion. Ito’s formula. Martingales. Stochastic differential equations. The Black–Scholes equation. Optimal stopping. American options.
Students will learn basic concepts of probability spaces: -algebras, distributions, proba-
bility densities, independence, conditional expectations.
2. Students will learn the Brownian Motion, Wiener measure, Stochastic processes, and Ito's
integrals.
3. Students will learn Stochastic di
erential equations, di
usion processes, Markov proper-
ties, Kolmogorov's backward equation, the generator of an Ito di
usion, boundary value
problems, the Dirichlet problem, the Poisson problem, and the Girsanov theorem.
4. Students will learn financial markets with mathematical interpretations, portfolio and
arbitrage, attainability and completeness, Black-Scholes equation and its solution formula,
and European options.
5. Students will learn optimal stopping theory, American options, PDEs with free boundaries,
and variational inequalities.
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Key: 5640