Alain Bensoussan

Lars Magnus Ericsson Chair
Professor - Management
Tags: Supply Chain Operations Management

Professional Preparation

Ph.D. - Mathematics
University of Paris, France - 1969
M.S. - Economics and Statistics
Ecole Nationale de la Statistique et de lAdministration Economique - 1965
M.S. - Mathematics and Sciences
Ecole Polytechnique - 1962

Research Areas

Description of the Research Works

1 INTRODUCTION
Trained in Control Theory, my main field of expertise consists in connecting methods from Analysis and Stochastic Processes in view of solving concrete problems of applied mathematics, not necessarily arising from Control.
In the course of my scientific career I have supervised around 20 PhD students.


2 DESCRIPTION OF RESULTS
2.1 STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

I was among the early initiators of the theory of stochastic PDE in the sense of Ito. I worked in particular, alone or in cooperation, on stochastic monotone equations, stochastic Navier-Stokes equations, stochastic variational inequalities, and more recently on stochastic inertial manifolds.
This theory has found some of its most interesting applications in the study of nonlinear filtering theory, where the work of my former student PARDOUX is a reference.
Note that numerical resolution is now within reach, which makes this field of research quite active and quite useful for applications.


2.2 FILTERING AND CONTROL OF STOCHASTIC DISTRIBUTED SYSTEMS
These problems have been at the origin of my research. In particular my thesis (under the supervision of J.L. LIONS) was devoted to Kalman filtering for linear systems with white noise inputs on both time and space. My main contribution was to make use of the theory of cylindrical measures of
Gelfand Vilenkin and L. Schwartz. This permits a rigorous approach to a large variety of problems, provided the model is linear.
I was in particular able to apply these techniques to a bidimensional model playing a role in image processing, or to the problem of optimal location of sensors.
In the problem of control, I contributed strongly to the theory of necessary conditions, and to a rigorous approach of Dynamic Programming via nonlinear semi-groups.
The main field of application concerns the stochastic control of systems with partial information, which naturally has a huge domain of applications.


2.3 OPTIMAL STOPPING, IMPULSE CONTROL, VARIATIONAL AND QUASI VARIATIONAL INEQUALITIES
I discovered, which is now standardly used, that variational inequalities corresponded to the dynamic programming treatment of optimal stopping, and then solved, with J. L. LIONS, the impulse control problem, via a new theory, called the theory of quasi variational inequalities. This has initiated a long and fruitful cooperation on this topic with J.L. LIONS and many colleagues and students. Many applications of this theory concern old and new problems of Operations Research and Management, as well as Physics and Mechanics.

2.4 REGULARITY of NONLINERAR SYSTEMS of ELLIPTIC and PARABOLIC PDE and APPLICATIONS
Stochastic Nash differential games lead to sytems of elliptic and parabolic PDE. The regularity of solutions is extremely important for obtaining a Nash point. This has motivated a longstanding cooperation with J. FREHSE, one of the worldwide specialists of the regularity of elliptic systems. I have also solved with him the ergodic case, which even in the case of one equation was open in its full generality.


2.5 ROBUST CONTROL and RISK-SENSITIVE CONTROL
My interest for this domain stems from its connection with the field of Risk sensitive stochastic control. In fact, I first solved with J. VAN SCHUPPEN the problem of finding a sufficient statistics(of the same size as the the state, which was an open problem) for the LEG (Linear ExponentialGaussian) control. More recently, in cooperation with J. BARAS and R. ELLIOTT, for the partial information case, and H. NAGAI and J. FREHSE for the full information case, I have contributed several results to justify some earlier formal treatment. The connection between robust control and risk sensitive control can be best seen through small noise introduction and singular perturbations. This is a field of very active research worldwide, by the broadness of the applications and the use of many mathematical techniques. It is one of my current research areas.


2.6 EXACT CONTROLLABILITY

After the introduction of the HUM method by J. L. LIONS, and its use by many authors, I got interested in developing a general theory of exact controllability for infinite dimensional systems,where the dynamics is driven by a skew-symmetric operator. In this way, one can unify most of the existing results concerning wave equations, Maxwell equations, ...


2.7 HOMOGENIZATION

Initiated by the probabilistic interpretation of homogenization, my interest in this domain has widened into an important cooperation with J.L. LIONS and G. PAPANICOLAOU, where we have developed many general approaches to this very fruitful theory.
More recently with L. BOCCARDO and F. MURAT I have considered the homogenization of Bellman equations, and with G. BLANKENSHIP the case of random homogenization.


2.8 REGULAR and SINGULAR PERTURBATIONS

Homogenization can be viewed as a particular situation of singular perturbations. But of course many other situations can be considered. It was natural for me to be interested in their application to Control theory, both deterministic and stochastic, and in the latter case with full or partial information. Many particularly useful results can be obtained in the case of partial information, where one can derive approximate but accurate finite dimensional feedback laws, where the optimal one is infinite dimensional.


2.9 SPECIFIC PROBLEMS in OPERATIONS MANAGEMENT and in FINANCE

Since Control Theory has a lot of applications in many areas of Quantitative Management, I have cooperated with several specialists of the field to obtain the solution of concrete problems. My current interest lies in Operations Management and in Finance. I have been working in the design of complex options with M. CROUHY and D. GALAI. More recently, with my student H. Julien, I have investigated models of options for incomplete markets, where the incompleteness arises from ”frictions” in the management of portfolios. Another approach to this problem has been developed with N. TOUZI and J. L. MENALDI, using penalty approximations and Viscosity methods. Since I joined UTD, the University of Texas at Dallas, I have been working on Inventory Control problems, with S. Sethi, M. Cakanyldirim, and PhD students. Our research focuses on stochastic models with partial information ( a field where little is available ), on service constraint models, on s, S policies. I have been also involved , jointly with S. SETHI, in models of Economic Growth developed by K.J. ARROW and al., taking into account population growth aspects.

Publications

Handbook in Mathematical Finance. With Q. Zhang. Elsevier. Forthcoming. forthcoming - Publication
Diagnostic Systems, Optimal Maintenance, Knowledge Based Systems. With R. Mookerjee, V. Mookerjee, and W. Yue. Management Science. Forthcoming. forthcoming - Publication
Forecasting the energy produced by a windmill on a yearly basis, Stochastic Environmental Research and Risk Assessment (SERRA) (online March 2012) with P.R. BERTRAND AND A. BROUSTE. 2012 - Publication
Existence and Compactness for Weak Solutions to Bellman Systems with Critical Growth, AIMS Journals (DCDS-B), vol. 17, no. 6, (September 2012, online May 2012) with M. BULEK and J. FREHSE. 2012 - Publication
When Do Firms Invest in Privacy-Preserving Technologies? E-Letter of Multimedia Communications Technical Committee (MMTC), IEEE Communications Society, 6(4), April 2011, pp. 15-17, with S. HOE AND M. KANTARCIOGLU. 2011 - Publication
Real Options and Variational Inequalities, in Advances in Financial Engineering, Hyeng Kuen Koo and Jaeyoung Sung (Eds.), IOS Press, with S. HOE and H-K KOO. 2011 - Publication
Dynamic Programming and Inventory Control (IOS Press September 2011) Vol. 3 Studies in Probability, Optimization and Statistics. 2011 - Publication
Average Cost Optimality in Inventory Models with Dynamic Information Delays, IEEE Transactions on Automatic Control, 56(12) (December 2011) pp. 2869-2882 with M. AKANYILDIRIM, S.P. SETHI, M. WANG, and H. ZHANG. ISSN: 0018-9286 2011 - Publication
The Genuine Savings Criterion and the Value of Population in an Economy with Endogenous Population Changes. Optimal Control of Age-structured Population in Economy, Demography, and the Environment. With K.J. Arrow, Q. Feng, and S.P. Sethi. Forthcoming. 2011 - Publication
Computation of Approximate Optimal Policies in Partially Observed Inventory Model with Rain Checks, Automatica, 47(8), (27 July 2011 online), pp. 1589-1604, with M. ÇAKANYILDIRIM, J.A. MINJAREZ-SOSA, S.P. SETHI and RUI XIA SHI. 2011 - Publication

Appointments

Director
University of Texas at Dallas [2004–Present]
Distinguished Research Professor
University of Texas at Dallas [2004–Present]
Emeritus Professor
University of Paris Dauphine [2004–Present]
Chairman
ESA Council (European Space Agency) [1999–2002]
President
CNES (Centre National d'Etudes Spatiales) [1996–2003]
President of INRIA
Institut National de Recherche en Informatique et Automatique [1984–1996]
Part time Professor
Ecole Normale Superieure [1980–1985]
Director
European Institute for advanced Studies in Management, Brussels [1975–1977]
Chairman
Mathematics Department of the University Paris Dauphine [1975–1977]
Professor
European Institute for advanced Studies in Management, Brussels [1971–1973]

Additional Information

Awards and Recognition
  • Charter Fellow, Society for Industrial and Applied Mathematics (SIAM), 2009.
  • Member of the French Academy of Sciences, 2003 Correspondent Member, 1986
  • Legion d’Honneur (Officier), 2003
  • BundesVerdienst Kreuz (Officier), 2003
  • NASA, Distinguished Public Service Medal, 2001
  • Ordre National du Merite (Commandeur), 2000
  • Member of the French Academy of Technology, 2000
  • Member of the International Academy of Astronautics, 1999
  • Member of Academia Europae, 1985
  • Fellow IEEE, 1985
  • Von Humboldt Prize, 1984
Professional Organizations
  • Institute of Electrical and Electronics Engineers
  • Society for Industrial and Applied Mathematics
  • The Institute For Operations Research and The Management Sciences (INFORMS)
SCIENTIFIC RESPONSIBILITIES
  • Vice Chairman of the IFAC ”Mathematics of control” Committee from 1978 to 1981.
  • Member of the organizing Committee of the IFAC World Congress (1981).
  • Member of the selection Committee for the session Control Theory and Optimization, International Congress of Mathematics, Helsinki 1978 and Chairman for the same session, Warsaw 1982.
  • Chairman of AFIRST, Franco-Israeli Association for Science and Technology from 1992 to March 1999.
  • Member of the Advisory Council of the Institute for Systems Research, University of Maryland.
  • Member of the Board of the Pitman Advanced Publishing Program in Mathematics.
  • Member of the Advisory Board of Mathematical Finance.
  • Editor in Chief of Asymptotic Analysis Journal (IOS Press).
  • Member of the Editorial Board of the following journals
    • Journal of Applied Mathematics and Optimization
    • Journal of Nonlinear Analysis
    • Numerical Functional Analysis and Applications
    • Policy Analysis and Information Systems
    • Sciences de Gestion
    • Systems and Control Letters
    • Acta Applicandae Mathematicae
    • Stochastic Analysis and Applications
    • Control Theory and Advanced Technology (C-TAT)
    • International Journal on Stochastic Hydrology and Hydraulics
    • Kybernetes
    • Optimal Control - Applications and Methods
    • Applied Mathematics Letters
    • Progress in Systems and Control Theory
    • Mathematical Models and Methods in Applied Sciences (M3AS)
    • Nonlinear Functional Analysis and Control Theory
    • Applied Mathematical Finance

News Articles

Grant Will Fund Studies in the Physics Behind Decision-Making
How are your decisions influenced by those of other people? And how do your decisions affect others?

An emerging area of research aims to answer questions about individual decision-making within very large populations. Called mean field game theory, the research seeks to explain, model and ultimately make predictions about behavior.
Dr. Alain Bensoussan
, an Ashbel Smith Professor in the Naveen Jindal School of Management, has received a $339,570, three-year grant from the National Science Foundation for a research project to study a theory called “Mean Field Games, Mean Field Type Control and Extensions.”