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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.

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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Course Attribute

Key: 5640