Philip Protter, Statistics Department, Columbia University

    Philip Protter

Publications          Books          Curriculum Vitae          Home

   

Research Areas:

    Mathematical Finance Theory
    Stochastic Numerical Analysis
    Stochastic Analysis and Its Applications
    Weak Convergence
    Markov Process Theory
    Filtering Theory
    Eclectic Papers

   

Mathematical Finance Theory

  1. The Financial Meltdown, Matapli, 87, 61-68, 2008. Also reprinted in Gazette de la Société Mathématique de France, 119, 76-92, January, 2009.
  2. (with Kiseop Lee) Hedging Claims with Feedback Jumps in the Price Process, Communications on Stochastic Analysis, 2, 125-143, 2008 (Special issue dedicated to Leonard Gross).
  3. (with R. Jarrow) Forward and Futures Prices with Bubbles, submitted for publication.
  4. (with Soumik Pal) Analysis of Strict Local Martingales via h-Tranforms, submitted for publication.
  5. (with R. Jarrow and K. Shimbo) Asset Price Bubbles in Incomplete Markets, to appear in Mathematical Finance.
  6. The Work of Kyosi Itô, Notices of the American Mathematics Society, 54 744-745, 2007.
  7. (with J. Jacod) Risk Neutral Compatibility with Option Prices, to appear in Finance and Stochastics.
  8. (with K. Shimbo) No Arbitrage and General Semimartingales, Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz, IMS Lecture Notes - Monograph Series 4, 267-283, 2008.
  9. (with R. Jarrow and K. Shimbo) Asset Price Bubbles in Complete Markets, Advances in Mathematical Finance, Springer-Verlag, M.C. Fu et al, eds., 97-122, 2007. (Volume in honor of Dilip Madan)
  10. (with R. Jarrow and H. Sayit) No Arbitrage without Semimartingales, to appear in the Annals of Applied Probability.
  11. (with R. Jarrow and D. Sezer) Information Reduction via Level Crossings in a Credit Risk Model, Finance and Stochastics, 11, 195-212, 2007.
  12. (with R. Jarrow) An Introduction to Financial Asset Pricing, Handbook in Operations Research and Management Science: Financial Engineering, 15, 13-69, J. Birge and V. Linetsky, eds., North Holland, 2007.
  13. (with R. Jarrow) Liquidity Risk and Option Pricing Theory, Handbook in Operations Research and Management Science: Financial Engineering, 15, 727-762, J. Birge and V. Linetsky, eds., North Holland, 2007.
  14. (with R. Jarrow) Liquidity Risk and Risk Measure Computation, to appear in Review of Futures Markets.
  15. (with U. Cetin, R. Jarrow, and M. Warachka) Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence, Review of Financial Studies 19; 493-529, 2006.
  16. (with R. Jarrow) Structural versus Reduced Form Models: A New Information Based Perspective, Journal of Investment Management 2; 34-43, 2004.
  17. (with R. Jarrow) Large Traders, Hidden Arbitrage, and Complete Markets, Journal of Banking and Finance, 29, 2803-2820, 2005.
  18. (with R. Jarrow) A Short History of Stochastic Integration and Mathematical Finance: The Early Years, 1880-1970, In The Herman Rubin Festschrift, IMS Lecture Notes 45 ; 75-91, 2004.
  19. (with U. Cetin and R. Jarrow) Liquidity Risk and Arbitrage Pricing Theory, Finance and Stochastics 8; 311-341, 2004.
  20. (with U. Cetin, R. Jarrow, and Y. Yildirim) Modeling Credit Risk with Partial Information, Annals of Applied Probability 14; 1167-1178, 2004.
  21. (with E. Clement and D. Lamberton) An Analysis of a Least Squares Regression Algorithm for American Option Pricing, Finance and Stochastics 17; 448-471, 2002.
  22. A Partial Introduction to Financial Asset Pricing Theory, Stochastic Processes and Their Applications 91; 169-203, 2001.
  23. (with Jean Jacod and Sylvie Méléard) Martingale Representation: Formulas and Robustness, Annals of Probability 28; 1747-1780, 2000.
  24. (with Dritschel, Michael) Complete Markets with Discontinuous Security Price, Finance and Stochastics 3; 203-214, 1999.
  25. (with Föllmer, H.and Shiryaev, A.N.) Quadratic Covariation and An Extension of Itô's Formula, Bernoulli 1; 149-169, 1995.
  26. (with Ma J. and Yong J.) Solving Forward-Backward Stochastic Differential Equations Explicitly-a Four Step Scheme, Proba. Th. Rel. Fields 98; 339-359, 1994.
  27. (with Duffie D.) The Boundary Between Discrete and Continuous Time Finance: Weak Convergence of the Financial Gain Process, J. of Mathematical Finance 2; 1-15, 1992.
  28. A book review of the book Mathematics for Finance: An Introduction to Financial Engineering, by M. Capinski and T. Zastawniak, Springer-Verlag, The American Mathematical Monthly 111; 923-926, 2004.
  29. A book review of the book Louis Bachelier's Theory of Speculation: The Origins of Modern Finance, by M.H.A. Davis and Alison Etheridge, Princeton University Press, 2006 The Bulletin of the American Mathematical Society 45; 657-660, 2008.

   

Stochastic Numerical Analysis

  1. (with Jean Jacod, Tom Kurtz and Sylvie Méléard) The Approximate Euler Method for Lévy Driven Stochastic Differential Equations, Annales de l'Institut Henri Poincaré, Special issue devoted to the memory of P.A. Meyer (En Hommage à Paul-André Meyer),41; 523-558, 2005
  2. (with Jin Ma, Jaime San Martin, and Soledad Torres) Numerical Method for Backward Stochastic Differential Equations, Annals of Applied Probability 12; 302-316, 2002
  3. (with Del Moral, Pierre and Jacod, Jean) The Monte- Carlo method for filtering with discrete time observations, Probability Theory and Related Fields 120; 346-368, 2001
  4. (with Jacod, Jean) Asymptotic Error Distributions for the Euler Method for Stochastic Differential Equations, Ann. Proba 26; 267-307, 1998
  5. (with Tom Kurtz) Limit theorems for solutions of stochastic equations II, CIME School in Probability, Springer Lecture Notes in Mathematics, 1627;197-285, 1996
  6. (with Tom Kurtz) Limit theorems for solutions of stochastic equations I, CIME School in Probability, Springer Lecture Notes in Mathematics, 1627;1-41, 1996
  7. (with D. Talay) The Euler scheme for Lévy driven stochastic differential equations, Ann. Proba 25; 393-423, 1997.
  8. (with J. Douglas, Jr. and J. Ma) Numerical methods for forward-backward stochastic differential equations, Ann. Applied Proba 6; 940-968, 1996.
  9. (with Ma J. and Yong J.) Solving Forward-Backward Stochastic Differential Equations Explicitly-a Four Step Scheme, Proba. Th. Rel. Fields 98; 339-359, 1994.
  10. (with A. Kohatsu-Higa) The Euler Scheme for SDEs driven by Semimartingales, in Stochastic Analysis on Infinite Dimensional Spaces, (H. Kunita and H.H. Kuo, eds.), Pitman, 141-151, 1994.
  11. (with Jacod J.) A Remark on the Weak Convergence of Processes in the Skorohod Topology, J. Theoretical Probability 6; 463-472, 1993.
  12. (with Kurtz T.G.) Wong-Zakai Corrections, Random Evolutions, and Numerical Schemes for SDEs, in Stochastic Analysis , Academic Press; 331-346, 1991.
  13. (with Kurtz T.G.) Weak Limit Theorems for Stochastic Integrals and Stochastic Differential Equations, Annals of Probability 19; 1035-1070, 1991.

   

Stochastic Analysis and Its Applications

  1. (with J. Jacod) Probability Essentials, Corrected Second Edition, Springer Verlag, 2004.
  2. (with Jin Ma and Jianfeng Zhang) Explicit form and path regularity of martingale representations, Lévy processes, 1627;337-360, Birkhäuser Boston, Boston, MA, 2001
  3. (with Jean Jacod and Sylvie Méléard) Martingale Representation: Formulas and Robustness, Annals of Probability 28; 1747-1780, 2000
  4. (with H. Föllmer) An extension of Itô’s formula in n dimensions, Probability Theory and Related Fields 116; 1-20, 2000.
  5. (with Ma, J. and San Martin, J.) Anticipating stochastic integrals for martingales, Bernoulli4; 81-114, 1998.
  6. (with Jacod, Jean) Asymptotic Error Distributions for the Euler Method for Stochastic Differential Equations, Ann. Proba 26; 267-307, 1998
  7. (with Tom Kurtz) Limit theorems for solutions of stochastic equations II, CIME School in Probability, Springer Lecture Notes in Mathematics, 1627;197-285, 1996
  8. (with Tom Kurtz) Limit theorems for solutions of stochastic equations I, CIME School in Probability, Springer Lecture Notes in Mathematics, 1627;1-41, 1996
  9. (with D. Talay) The Euler scheme for Lévy driven stochastic differential equations, Ann. Proba 25; 393-423, 1997.
  10. (with J. Douglas, Jr. and J. Ma) Numerical methods for forward-backward stochastic differential equations, Ann. Applied Proba 6; 940-968, 1996.
  11. (with D. Nualart) Skorohod integral for a product of two stochastic processes, J. Theoretical Probability, 9 1029-1037, 1996.
  12. (with O'Cinneide C.) An Elementary Approach to Naturality, Predictability, and the Fundamental Theorem of Local Martingales, Purdue Statistics Department Technical Report
  13. (with Föllmer, H.and Shiryaev, A.N.) Quadratic Covariation and An Extension of Ito's Formula, Bernoulli 1; 149-169, 1995.
  14. (with Kurtz T.G. and Pardoux E.) Stratonovich Stochastic Differential Equations Driven by General Semimartingales, Annales Inst. H. Poincaré 31; 351-377, 1995.
  15. (with Ahn H.) A Remark on Stochastic Integration, in Séminaire de Probabilités XXVIII, Springer Lect. Notes in Math 1583; 312-315, 1994.
  16. (with Léon, J.) Some Formulas for Anticipative Girsanov Transformations, in Chaos Expansion, Multiple Wiener-Itô Integrals and Their Applications, (C. Houdre and V. Perez-Abreu, eds.) CRC press (pp. 267-292), 1994.
  17. (with San Martin J.) General Change of Variables Formulas for Semimartingales in One and Finite Dimensions, Proba. Th. Rel. Fields 97; 363-381, 1993.
  18. (with Jacod J.) A Remark on the Weak Convergence of Processes in the Skorohod Topology, J. Theoretical Probability 6; 463-472, 1993.
  19. (with Carlen E.) On Semimartingale Decompositions of Convex Functions of Semimartingales, Illinois J. Math, 36; 420-427, 1992.
  20. (with Jacod J.) Une Remarque sur les Equations Differentielles Stochastiques à Solutions Markoviennes, Séminaire de Probabilités XXV, Springer Lect. Notes in Math. 1485; 138-139, 1991.
  21. (with Kurtz T.G.) Characterizing the Weak Convergence of Stochastic Integrals, in Stochastic Analysis (M. Barlow and N. Bingham, eds.); 255-259, 1991.
  22. (with Kurtz T.G.) Weak Limit Theorems for Stochastic Integrals and Stochastic Differential Equations, Annals of Probability 19; 1035-1070, 1991.
  23. (with Kurtz T.G.) Wong-Zakai Corrections, Random Evolutions, and Numerical Schemes for SDEs, in Stochastic Analysis , Academic Press; 331-346, 1991.

   

Weak Convergence

  1. (with Jean Jacod and Sylvie Méléard) Martingale Representation: Formulas and Robustness, Annals of Probability, 28, 1747-1780, 2000 .
  2. (with Del Moral, Pierre and Jacod, Jean) The Monte- Carlo method for filtering with discrete time observations, Probability Theory and Related Fields, 120, 346-368, 2001 .
  3. (with Jacod, Jean) Asymptotic Error Distributions for the Euler Method for Stochastic Differential Equations, Ann. Proba 26; 267-307, 1998
  4. (with Tom Kurtz) Limit theorems for solutions of stochastic equations II, CIME School in Probability, Springer Lecture Notes in Mathematics, 1627;197-285, 1996
  5. (with Tom Kurtz) Limit theorems for solutions of stochastic equations I, CIME School in Probability, Springer Lecture Notes in Mathematics, 1627;1-41, 1996
  6. (with D. Talay) The Euler scheme for Lévy driven stochastic differential equations, Ann. Proba 25; 393-423, 1997.
  7. (with J. Douglas, Jr. and J. Ma) Numerical methods for forward-backward stochastic differential equations, Ann. Applied Proba 6; 940-968, 1996.
  8. (with Kurtz T.G. and Pardoux E.) Stratonovich Stochastic Differential Equations Driven by General Semimartingales, Annales Inst. H. Poincaré 31; 351-377, 1995.
  9. (with Jacod J.) A Remark on the Weak Convergence of Processes in the Skorohod Topology, J. Theoretical Probability 6; 463-472, 1993. li> (with Duffie D.) The Boundary Between Discrete and Continuous Time Finance: Weak Convergence of the Financial Gain Process, J. of Mathematical Finance 2; 1-15, 1992.
  10. (with Kurtz T.G.) Characterizing the Weak Convergence of Stochastic Integrals, in Stochastic Analysis (M. Barlow and N. Bingham, eds.); 255-259, 1991.
  11. (with Kurtz T.G.) Weak Limit Theorems for Stochastic Integrals and Stochastic Differential Equations, Annals of Probability 19; 1035-1070, 1991.
  12. (with Kurtz T.G.) Wong-Zakai Corrections, Random Evolutions, and Numerical Schemes for SDEs, in Stochastic Analysis , Academic Press; 331-346, 1991.
  13. Weak Convergence in Analysis, in White Noise Analysis , World Scientific; 331-336, 1990.

   

Markov Process Theory

  1. (with Jean Jacod and Sylvie Méléard) Martingale Representation: Formulas and Robustness, submitted for publication.
  2. (with Del Moral, Pierre and Jacod, Jean) The Monte- Carlo method for filtering with discrete time observations, submitted for publication.
  3. (with Jacod, Jean) Asymptotic Error Distributions for the Euler Method for Stochastic Differential Equations, Ann. Proba 26; 267-307, 1998
  4. (with Tom Kurtz) Limit theorems for solutions of stochastic equations II, CIME School in Probability, Springer Lecture Notes in Mathematics, 1627;197-285, 1996
  5. (with D. Talay) The Euler scheme for Lévy driven stochastic differential equations, Ann. Proba 25; 393-423, 1997.
  6. (with Jacod J.) Une Remarque sur les Equations Differentielles Stochastiques à Solutions Markoviennes, Séminaire de Probabilités XXV, Springer Lect. Notes in Math. 1485; 138-139, 1991.
  7. (with Kurtz T.G.) Weak Limit Theorems for Stochastic Integrals and Stochastic Differential Equations, Annals of Probability 19; 1035-1070, 1991.

   

Filtering Theory

  1. (with Jean Jacod and Sylvie Méléard) Martingale Representation: Formulas and Robustness, submitted for publication.
  2. (with Del Moral, Pierre and Jacod, Jean) The Monte- Carlo method for filtering with discrete time observations, submitted for publication.
  3. (with Tom Kurtz) Limit theorems for solutions of stochastic equations II, CIME School in Probability, Springer Lecture Notes in Mathematics, 1627;197-285, 1996

   

Eclectic Papers

  1. (with D. Burkholder) Joseph Leo Doob, 1910--2004, Stochastic Processes and Their Applications. 115; 1061-1072, 2005.
  2. A book review of the book Mathematics for Finance: An Introduction to Financial Engineering, by M. Capinski and T. Zastawniak, Springer-Verlag, The American Mathematical Monthly 111; 923-926, 2004.


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