STAT 598F. Modeling with Jump Processes and Applications to Mathematical Finance.

• Office: Math 542
• Office hours: F 1:30 - 2:30, or by appointment
• Phone: (765) 494 6036
• E-mail: figueroa@stat.purdue.edu (best way to contact me)

• Description.
• A review paper on financial models based on Levy processes.
• An interesting motivational paper: Empirical properties of asset returns: stylized facts and statistical issues by Rama Cont.
• Levy processes and Poisson random measures.

• Old course's syllabus. (to be updated).
• Previous tentative final project topics:
  • Topics about stochastic control and portfolio optimization under jumps.
  Reference: Applied Stochastic Control of Jump Diffusions by Sulem and Oksendal.
  • Topics about inverse problems and model calibration.
  Some References: (1) Chapter 13 in Cont and Tankov. (2) Spectral calibration of exponential Levy models by Belomestny and Reiss.
  • Topics related to Malliavin Calculus with jumps
  Some possible references: (Order is irrelevant)
  (1) Computations of Greeks in a market with jumps via the Malliavin calculus by El-Khatib and Privault. Finance Stoch., 8(2):161-179, 2004.
  (2) Malliavin Monte Carlo Greeks for jump diffusions by Davis and Johansson in Stochastic Process. Appl., 116(1):101-129, 2006.
  (3) Discrete time approximation of decoupled Forward-Backward SDE with jumps by Bouchard and Elie in Stochastic Processes and their Applications 118, 1 (2008) 53-75.
  (4) Stein's method and normal approximation of Poisson functionals by Peccati, Sole, Taqqu and Utzet. Available at www.geocities.com/giovannipeccati/.
  • Self-similar additive models for asset prices (paper by Carr, Geman, Madam, and Yor 2007).
  • Stochastic volatility models driven by Levy processes (paper by Carr, Geman, Madan, and Yor on time-changed Levy models and paper by Barndorff-Nielsen and Shephard on non-Gaussian OU based models)
  • Estimation of the integrated volatility in jumps-diffusion models under microstructure noise market.
  • Testing of jumps in semimartingale models with jumps.

The content of this page and any opinions expressed therein are solely those of Jose E. Figueroa-Lopez.