Jose E. Figueroa-Lopez Assistant Professor of Statistics Purdue University West Lafayette, IN 47907 Office: Math 543. Phone: (765) 494 6036 E-mail: figueroa@stat.purdue.edu

Research Interests :

• Mathematical finance: Nonparametric estimation methods and portfolio optimization problems in continuous-time models. Emphasis on Levy driven and jump-diffusion models.
• Probability and Stochastic processes: Stochastic control, stochastic analysis, and simulation.
• Statistics: Nonparametric estimation using projection estimation, model selection, and adaptive methods.
• Information and coding theory: Concentration inequalities applied to data compression.

Teaching:

• Spring 2010:
• STAT 598F. Modeling with Jump Processes and Applications to Mathematical Finance
• STAT 511. Statistical Methods.
• Fall 2009:
• MATH 516/STAT 541. Advanced Probability and Options, with numerical methods.
• Spring 2009:
  • MATH 515/STAT 540. Mathematics of Finance.
  • Financial modeling with jump processes.

Research:

• Articles:
  • State-dependent utility maximization in Levy markets (with J. Ma). To appear in the International Journal of Stochastic Analysis, 2010.
  • Jump-diffusion models driven by Levy processes. To appear in the Handbook of Computational Finance, Jin-Chuan Duan, James E. Gentle, and Wolfgang Hardle (eds.). Springer, 2010.
  • Nonparametric estimation of time-changed Levy models under high-frequency data . Advances in Applied Probability vol. 41, number 4, pp. 1161-1188, 2009.
  • Small-time expansions for the transition distribution of Levy processes (with C. Houdré). Stochastic Processes and their Applications 119 pp. 3862-3889, 2009. dx.doi.org/10.1016/j.spa.2009.09.002
  • Nonparametric estimation for Levy models based on discrete-sampling. IMS Lecture Notes-Monograph Series (LNMS). Optimality: The Third Erich L. Lehmann Symposium. Volume 57, 117-146, 2009.
  • Small-time moment asymptotics for Levy processes. Statistics and Probability Letters 78, 3355-3365, 2008. DOI:10.1016/j.spl.2008.07.012.
  • Risk bounds for the non-parametric estimation of Levy processes (with C. Houdré). In: High Dimensional Probability IV. IMS Lecture Notes (editors: E. Gine, V. Kolchinskii, W. Li, J. Zinn), 2006.
  • On the asymptotic redundancy of lossless block coding with two codeword lengths (with C. Houdré). In IEEE Transactions on Information Theory, 688-692, Vol. 51, 2005.

• Some Preprints and current work:
  • Sieve-based confidence intervals and bands for Levy densities. Revised version: December 2009. Submitted.
  • Approximations for the distributions of bounded variation Levy processes. This version: January 2010. Submitted.
  • Central limit theorems for the non-parametric estimation of time-changed L\'evy models. This version: October 2009. Submitted.
  • Statistical estimation of Levy-type stochastic volatility models. This version: February 2010. Submitted.

• Other manuscripts:
  • A selected survey of portfolio optimization problems.
  • An overview of a nonparametric estimation method for Levy processes (with C. Houdre).

Research Funding:

Curriculum Vitae

Some interesting links:

• Maths and markets. Financial Times (03/21/2009) writes: "For the future we need more - and better - maths to underpin individual banks and the enhanced regulatory regime that will oversee them. Some of the expertise required is already out there, in universities, waiting to be put to use."

Talks:

• Nonparametric estimation for a Time-changed Levy Model. Research Colloquium, Purdue University, Spring 2010.

• Accurate asset price modeling and related statistical problems under microstructure noise. VIGRE Seminar, Purdue University, Fall 2009.

• Nonparametric estimation of time-changed L\'evy models. Applied Mathematics Colloquia, Illinois Institute of Technology, November 2009. Also presented at the Mathematical Finance and Probability Seminar, Rutgers University, October 2009.

• Optimal portfolios and admissible strategies in a Levy market Stochastic Analysis at Purdue '09 Workshop 2009.

• Some estimation problems related to time-changed L\'evy models. Mathematical statistics seminar. Department of Statistics. Purdue University.

• Sieve-based confidence intervals and bands for Levy densities. Mathematical statistics seminar. Department of Statistics. Purdue University.

• Non-parametric methods for L\'evy-based financial models. Workshop on Infinitely Divisible Processes. CIMAT. Guanajuato, Mexico. March 2009.

• Modeling and estimating the dynamics of asset prices. VIGRE Seminar, Purdue University, Fall 2008.

• Model selection for Levy processes based on discrete-sampling. The fifth international conference on High Dimensional Probabilty. CIRM, Luminy, France. May, 2008.

• State-dependent utility maximization in markets driven by additive Levy processes . AMS Spring Central Section Meeting, Bloomington, IN. Special Session on Financial Mathematics, April, 2008.

• State-dependent utility maximization in Levy markets. Seminar on Mathematical Finance and Financial Engineering. Georgia Tech. Department of Mathematics. Spring 2008.

• Introduction to pricing methods for credit derivatives. Computationa Finance Seminar, Purdue University, Spring 2008.

• Modeling and estimation of the dynamics of asset prices. VIGRE Seminar, Purdue University, Fall 2007.

• Model selection for Levy processes based on discrete-sampling . Statistics Research Colloquium, Purdue University, Fall 2007.

• Non-parametric estimation for some models driven by Levy processes,The Third Erich L. Lehmann Symposium, 2007.

• State-dependent utility maximization in Levy markets, Kent-Purdue Mini Symposium on Financial Mathematics, 2007

• State-dependent utility maximization in Levy markets, Probability and statistics seminar, USC, Feb. 2007.

• Notes, Seminar "Topics in Financial Mathematics", UCSB, Jan. 2007.

• Calibration and portfolio optimization issues in asset price modelling driven by Levy processes, ORIE Colloquium, Cornell, Jan. 2007.

• Estimation Methods for Levy based models of asset prices, Financial Mathematics Seminar, Statistics Department, UCSB, Oct. 2006
  • Slides Talk 1
  • Slides Talk 2
  • Notes

• Nonparametric methods for financial models driven by Levy processes, Special Colloquium, Department of Statistics, Purdue University, Mar. 2006

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

Last modified: October 2009