Dr. Gunduz Caginalp

Professor of Mathematics, University of Pittsburgh

        caginalp [use at symbol] pitt [use period] edu     (412) 624-8339


Recent News Articles  (see also pitt.edu/~careycag)

Recent Papers

Riemann Zeta Function

Optimization Ultimatum Game (with S. Ho)

Recent papers with Carey Caginalp (www.pitt.edu/~careycag)  Cryptocurrencies:  Proc. National Academy of Sciences

Quotient of normals and fat tails: Physica A

Wilmott Cover Story Discussion with "Irrational Exuberance" author and Nobel Laureate Robert Shiller

Select new papers:  The Nonlinear Price Dynamics of Large US Equity ETFs (J. Econometrics) 

The most downloaded recent (60 days) paper in the Economics topic of SSRN (April 29, 2015)

Renormalization Methods for Higher Order DEs (J. Physics A)

    In the news....

          Science   NY Times   SIAM News   Wilmott Interview  Chief Investment Officer
          Shanghai Evening Post  Texas Enterprise
   Pitt Magazine



Previous Positions



Graduate Courses Taught

Mathematical modeling, numerical analysis of partial differential equations, ordinary differential equations 1 and 2, partial differential equations 1 and 2, linear and nonlinear elliptic differential equations (advanced), nonlinear problems, physics of solidification, linear functional analysis 1 and 2, functional analysis with applications to nonlinear problems, advanced topics in differential equations, variational methods in nonlinear problems, mathematical physics:  statistical mechanics and quantum theory, renormalization and scaling theory, renormalization group in differential equations, mathematics of finance I (methods and optimization), III (derivatives and options) and IV (classical and behavioral finance), dynamics of financial markets.



Recent Graduate Students

E. Esenturk (2011) Post-doctoral Research Associate, Brown University August- December 2011, Pohang Math Inst, Postech Univ, S. Korea January 2012-2014, Research associate at Warwick University, UK 2015, Cambridge University current.

M. DeSantis (2011) Assistant Professor, Chapman University September 2011-current.

A. Duran (2006)  Assistant Professor, Math Dept, University of Michigan, Ann Arbor  2006-2010.; Assistant Professor, Istanbul Technical University 2010-current,

H. Merdan (2004) Visiting Assistant Professor, Illinois Institute of Technology 2004-2005), TOBB (Economics and Technology University)  Assistant Professor 2005, currently Professor of Applied Mathematics TOBB.

Y. B. Altundas (2002) IMA Postdoc 2002-2004, Senior Research Scientist at Schlumberger Research Labs



Research Highlights

Differential Equations and Optimization in Financial Markets
Statistical Methods in Financial Markets

Experimental Asset Markets and Modeling

Renormalization Group and Multiscaling Techniques in Differential Equations
Interface Problems and Phase Field Computations



Publication List as of August 2016  

Selected Papers



Papers Related to Experimental Economics (with 2002 Nobel Laureate Vernon Smith and David Porter)

Do Speculative Stocks Lower Prices and Increase Volatility of Value Stocks? (2002)

Financial Bubbles: Excess Cash, Momentum, and Incomplete Information (2001)

Momentum and Overreaction in Experimental Asset Markets (2000)

Overreaction, Momentum, Liquidity, and Price Bubbles in Laboratory and Field Asset Markets (with D. Porter and V. Smith 2000)

Initial Cash/Asset Ratio and Stock Prices: An Experimental Study (1998)


Mathematical Economics and Finance

Are Flash Crashes Caused by Instabilities Arising from Rapid Trading? (with M. DeSantis and D. Swigon 2011)

Multi-Group Asset Markets and Stability (with M. DeSantis 2011)

Nonlinear Stock Price Dynamics Nonlinear Analysis (with M. DeSantis 2011)

Stock Price Dynamics, Trend, ... Quantitative Finance (with M. DeSantis 2011)

Parameter Optimization for Differential Equations in Asset Price Forecasting (with A. Duran 2008)

Overreaction Diamonds: Precursors and Aftershocks for Significant Price Changes (with A. Duran 2007)

Asset Price Dynamics with Heterogeneous Groups (with H. Merdan 2007)

Nonlinear Price Evolution (2005)

The Dynamics of Trader Motivation in Asset Bubbles (with V. Ilieva 2005)

Derivation of Asset Price Equations Through Statistical Inference (with V. Ilieva, D. Porter, and V. Smith 2003)

Asset Flow and Momentum: Deterministic and Stochastic Equations (with D. Balenovich 1999)

The Predictive Power of Price Patterns (with Henry Laurent 1998)

Trend Based Asset Flow in Technical Analysis (with D. Balenovich 1996)

Statistical Inference and Modeling of Momentum in Stock Prices (with G. Constantine 1995)

A Theoretical Foundation for Technical Analysis (with D. Balenovich 1995)

Market Oscillations Induced by the Competition Between Value-Based and Trend-Based Investment Strategies (with D. Balenovich 1994)

Editorials For Journal of Behavioral Finance

Editorial "The Foundations of Experimental Economics and Applications to Behavioral Finance: The Contributions of Nobel Laureate Vernon Smith" (with K. McCabe, D. Porter 2003)


Editorial "Does the Market Have a Mind of Its Own, and Does It Get Carried Away with Excess Cash?" (2002)


Editorial "The Real Year 2000 Problem: Investor Psychology" (2001)


Large Scale Computations Using the Phase Field Equations

Velocity Selection in 3D Dendrites: Phase Field Computations and Microgravity Experiments (with Y. B. Altundas 2005)

Computations of Dendrites in 3-D and Comparison with Microgravity Experiments (with Y.B. Altundas 2003)

Phase Field Computations of Single-Needle Crystals, Crystal Growth and Motion by Mean Curvature (with E. A. Socolovsky 1994)

Efficient Computation of a Sharp Interface by Spreading via Phase Field Methods (with E. A. Socolovsky 1989)



Phase Field Alloys
An Analysis of Phase Field Alloys and Transition Regions (with W. Xie 1998)

A Derivation and Analysis of Phase Field Models of Thermal Alloys (with J. Jones 1995)

Phase Field and Sharp Interface Alloy Models (with W. Xie 1993)


Phase Field Model and Sharp Interface Limits

Phase Field Model .. Anisotropic and Non-local Interactions (with X. Chen and E. Esenturk 2011)

A Phase Field Model with Non-local and Anisotropic Potential MSMSE (with X. Chen and E. Esenturk 2011)

Numerical Tests of a Phase Field Model with Second Order Accuracy (with X. Chen and C. Eck 2008)

A Rapidly Converging Phase Field Model (with X. Chen and C. Eck 2006)
Rapidly Converging Phase Field Models via Second Order Asymptotic (with C. Eck 2005)

Convergence of Phase Field Model to Its Sharp Interface Limits (with X. Chen 1998)

Stefan and Hele-Shaw Type Models as Asymptotic Limits of the Phase Field Equations (1989)


Older Phase Field Papers

Existence of Travelling Waves for Phase Field Equations and
Convergence to Sharp Interface Models in the Singular Limit (with Y. Nishiura 1991)

A Derivation of a Phase Field Model with Fluid Properties (with J. Jones 1991) 

A Microscopc Derivation of Macroscopic Phase Boundary Problems (1990)

A Conserved Phase Field System; Implications for Kinetic Undercooling (1988)

Dynamics of Layered Interfaces arising from Phase Boundaries (with P. C. Fife 1988)

Phase Field Methods for Inter-facial Boundaries (with P. C. Fife 1986)

The Role of Microscopic Anisotropy in the Macroscopic Behavior of a Phase Boundary (1986)

An analysis of a Phase Field Model of a Free Boundary [submitted 1983, published 1986; Earlier version was Carnegie-Mellon Math Department Research Report 82-5 (1982)]




Renormalization and Multiscaling Applied to Decay, Blow-up and Extinction

SIAM Tutorial:Renormalization and Scaling in Applied Mathematics (2004)

Renormalization Group Methods for Nonlinear Parabolic Equations (with H. Merdan 2003)

Decay of Solutions to Nonlinear Parabolic Equations: Renormalization and Rigorous Results (with H. Merdan 2003)

A Renormalization Group Approach to Blow-up and Extinction Exponents (2001)

Renormalization and Scaling Methods for Nonlinear Parabolic Systems (1997)

A Renormalization Group Calculation of Anomalous Exponents for Nonlinear Diffusion (1996)


Renormalization and Multiscaling Applied to Interfaces 

Renormalization and Scaling Methods for Quasi-Static Interface Problems (with H. Merdan 2005)

The Transition Between Quasi-Static and Fully Dynamic for Interfaces (with H. Merdan 2004)

Renormalization Group Calculation of Late Stage Interface Dynamics (2001)

Dynamical Renormalization Group Calculation of a Two-Phase Sharp Interface Model (1999)

Link to Journal of Behavioral Finance (formerly Journal of Psychology and Financial Markets)


Link for papers posted on Social Sciences Research Network


Other Research Links

Math Department, University of Pittsburgh

International Foundation for Experimental Economics

Papers of Carey Caginalp

Last updated August 5, 2016