Course Description
This is a graduate course on stochastic calculus with emphasis on applications in finance. We introduce the basic concepts on continuous time stochastic processes: Brownian motion and Poisson processes, martingales and stopping times with game theory and finance examples. Then we construct the stochastic integral with respect to the Brownian motion, showing basic results including the change of variable formula, Girsanov theorem and martingale representation. We show how to use stochastic calculus to formulate and solve stochastic differential equations driven by Brownian motion. We present simple examples of equations and basic numerical schemes. We illustrate its use for pricing and hedging of derivative securities in the Black-Scholes model, including the relation with partial differential equations through Feynman-Kac formula and further applications to exotic options and interest rate models.
Instructor:
Professor of Mathematics, University of Kansas. Ph. D. in Mathematics, Universidad de Barcelona (1975). Professor Nualart’s research interests focus on the application of Malliavin calculus to a wide range of topics including regularity of probability laws, anticipating stochastic calculus, stochastic integral representations and central limit theorems for Gaussian functionals. His recent research deals with the stochastic calculus with respect to the fractional Brownian motion and related processes. Other fields of interest are stochastic partial differential equations, rough path analysis and mathematical finance. He has published his research in top journals, including Probability Theory Related Fields, Annals of Probability, Journal of Probability, Transactions of the America Mathematical Society, among others.
Dates
June 14, 15, 16, 17 and 20: 16:00-19:00
Venue
Universidad Carlos III de Madrid (Getafe Campus)
Calle Madrid, 126
Building 15,
Room 15.0.15 (Map)
Registration Fee
500 Euros*
*Fee covers the course and accompanying materials. The registration fee for students currently enrolled in a Ph.D. program is reduced to 300 Euros. Students may apply for scholarshipsby sending an application letter documenting the merits of their request to the Director of SSECO, Juan J. Dolado at instituto.economia@uc3m.es, indicating as subject “SSECO-scholarship”. Course attendees need to arrange and pay for their own lodging.
Scholarships Applications will not be considered after June 3, 2011.
Course Description
This is a graduate course on stochastic calculus with emphasis on applications in finance. We introduce the basic concepts on continuous time stochastic processes: Brownian motion and Poisson processes, martingales and stopping times with game theory and finance examples. Then we construct the stochastic integral with respect to the Brownian motion, showing basic results including the change of variable formula, Girsanov theorem and martingale representation. We show how to use stochastic calculus to formulate and solve stochastic differential equations driven by Brownian motion. We present simple examples of equations and basic numerical schemes. We illustrate its use for pricing and hedging of derivative securities in the Black-Scholes model, including the relation with partial differential equations through Feynman-Kac formula and further applications to exotic options and interest rate models.
Instructor:
Professor of Mathematics, University of Kansas. Ph. D. in Mathematics, Universidad de Barcelona (1975). Professor Nualart’s research interests focus on the application of Malliavin calculus to a wide range of topics including regularity of probability laws, anticipating stochastic calculus, stochastic integral representations and central limit theorems for Gaussian functionals. His recent research deals with the stochastic calculus with respect to the fractional Brownian motion and related processes. Other fields of interest are stochastic partial differential equations, rough path analysis and mathematical finance. He has published his research in top journals, including Probability Theory Related Fields, Annals of Probability, Journal of Probability, Transactions of the America Mathematical Society, among others.
Dates
June 14, 15, 16, 17 and 20: 16:00-19:00
Venue
Universidad Carlos III de Madrid (Getafe Campus)
Calle Madrid, 126
Building 15,
Room 15.0.15 (Map)
Registration Fee
500 Euros*
*Fee covers the course and accompanying materials. The registration fee for students currently enrolled in a Ph.D. program is reduced to 300 Euros. Students may apply for scholarshipsby sending an application letter documenting the merits of their request to the Director of SSECO, Juan J. Dolado at instituto.economia@uc3m.es, indicating as subject “SSECO-scholarship”. Course attendees need to arrange and pay for their own lodging.
Scholarships Applications will not be considered after June 3, 2011.