Gunduz Caginalp (died December 7th, 2021) was a Turkish-born American mathematician whose research has also contributed over 100 papers to physics, materials science and economics/finance journals, including two with Michael Fisher and nine with Nobel Laureate Vernon Smith.
He began his studies at Cornell University in 1970 and received an AB in 1973 "Cum Laude with Honors in All Subjects" and Phi Beta Kappa.
Caginalp's PhD in Applied Mathematics at Cornell University (with thesis advisor Professor Michael Fisher) focused on surface free energy.
Previous results by David Ruelle, Fisher, and Elliot Lieb in the 1960s had established that the free energy of a large system can be written as a product of the volume times a term
A key result of Caginalp's thesis [1,2,3] is the proof that the free energy, F, of a lattice system occupying a region
Shortly after his PhD, Caginalp joined the Mathematical Physics group of James Glimm (2002 National Medal of Science recipient) at The Rockefeller University.
In addition to working on mathematical statistical mechanics, he also proved existence theorems on nonlinear hyperbolic differential equations describing fluid flow.
In 1980, Caginalp was the first recipient of the Zeev Nehari position established at Carnegie-Mellon University's Mathematical Sciences Department.
He had published over fifty papers on the phase field equations in mathematics, physics and materials journals.
The focus of research in the mathematics and physics communities changed considerably during this period, and this perspective is widely used to derive macroscopic equations from a microscopic setting, as well as performing computations on dendritic growth and other phenomena.
However, the calculation of exact exponents in statistical mechanics showed that mean field theory was not reliable.
In 1980 there seemed to be ample reason to be skeptical of the idea that an order parameter could be used to describe a moving interface between two phases of a material.
Using the phase field idea to model solidification so that the physical parameters could be identified was originally undertaken in [4].
A number of papers in collaboration with Weiqing Xie* and James Jones [5,6] have extended the modeling to alloy solid-liquid interfaces.
Caginalp further developed these ideas so that one can calculate the decay (in space and time) of solutions to a heat equation with nonlinearity [13] that satisfies a dimensional condition.
The methods were also applied to interface problems and systems of parabolic differential equations with Huseyin Merdan*.
The efficient-market hypothesis (EMH) has been the dominant theory for financial markets for the past half century.
Behavioral finance has challenged this perspective, citing large market upheavals such as the high-tech bubble and bust of 1998–2003, etc.
The difficulty in establishing the key ideas of behavioral finance and economics has been the presence of "noise" in the market.
An early study by Caginalp and Constantine in 1995 showed that using the ratio of two clone closed-end funds, one can remove the noise associated with valuation.
Subsequent work with Ahmet Duran* [14] examined the data involving large deviations between the price and net asset value of closed end funds, finding strong evidence that there is a subsequent movement in the opposite direction (suggesting overreaction).
Dr. Vladimira Ilieva and Mark DeSantis* focused on large scale data studies that effectively subtracted out the changes due to the net asset value of closed end funds [15].
Using exchange traded funds (ETFs), they also showed (together with Akin Sayrak) that the concept of resistance—whereby a stock has retreats as it nears a yearly high—has strong statistical support [16].
The research shows the importance of two key ideas: (i) By compensating for much of the change in valuation, one can reduce the noise that obscures many behavioral and other influence on price dynamics; (ii) By examining nonlinearity (e.g., in the price trend effect) one can uncover influences that would be statistically insignificant upon examining only linear terms.
(I) Unlike the EMH, the model developed by Caginalp and collaborators since 1990 involves ingredients that were marginalized by the classical efficient market hypothesis: while price change depends on supply and demand for the asset (e.g., stock) the latter can depend on a variety of motivations and strategies, such as the recent price trend.
(III) In collaboration with Duran these equations were studied in terms of optimization of parameters, rendering them a useful tool for practical implementation.
(IV) More recently, David Swigon, DeSantis and Caginalp studied the stability of the asset flow equations and showed that instabilities, for example, flash crashes could occur as a result of traders utilizing momentum strategies together with shorter time scales [17, 18].
In the 1980s asset market experiments pioneered by Vernon Smith (2002 Economics Nobel Laureate) and collaborators provided a new tool to study microeconomics and finance.
Caginalp, Smith and David Porter largely resolved this paradox through the framework of the asset flow equations.
In particular, the bubble size (and more generally, the asset price) was highly correlated by the excess cash in the system, and momentum was also shown to be a factor [19].