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Abstracts and Talk Materials
New Mathematical Models in Economics and Finance
June 7 - 18, 2010


Erhan Bayraktar (University of Michigan)
http://www.math.lsa.umich.edu/~erhan/

Strict local martingale deflators and pricing American call-type options
June 15, 2010

We solve the problem of pricing and optimal exercise of American call-type options in markets which do not necessarily admit an equivalent local martingale measure. This resolves an open question proposed by Fernholz and Karatzas [Stochastic Portfolio Theory: A Survey, Handbook of Numerical Analysis, 15:89-168, 2009].

Joint work with Kostas Kardaras and Hao Xing. Available at http://arxiv.org/abs/0908.1082.

Steven A Bleiler (Portland State University)

Evaluating regulatory strategies for emmision abatement - An engineering approach
June 16, 2010


Guillaume Carlier (Université de Paris IX (Paris-Dauphine))
http://www.ceremade.dauphine.fr/~carlier/

Congested transport
June 11, 2010


Guillaume Carlier (Université de Paris IX (Paris-Dauphine))
http://www.ceremade.dauphine.fr/~carlier/

Monge-Kantorovich optimal transport problem
June 7, 2010


Guillaume Carlier (Université de Paris IX (Paris-Dauphine))
http://www.ceremade.dauphine.fr/~carlier/

Strictly convex transportation costs
June 8, 2010


Guillaume Carlier (Université de Paris IX (Paris-Dauphine))
http://www.ceremade.dauphine.fr/~carlier/

The case cost=distance
June 9, 2010


Guillaume Carlier (Université de Paris IX (Paris-Dauphine))
http://www.ceremade.dauphine.fr/~carlier/

Economic applications of optimal transport
June 10, 2010


Rene Carmona (Princeton University)
http://www.princeton.edu/~rcarmona/
Max Fehr (London School of Economics and Political Science)
http://www.ifor.math.ethz.ch/staff/maxfehr

Implementation of a simple model: first example
June 8, 2010


Rene Carmona (Princeton University)
http://www.princeton.edu/~rcarmona/

Stochastic optimization and first continuous time models of cap-and-trade schemes
June 11, 2010


Rene Carmona (Princeton University)
http://www.princeton.edu/~rcarmona/

Binary martingales and option pricing: 1) Reduced form models; 2) Perturbation methods
June 14, 2010


Rene Carmona (Princeton University)
http://www.princeton.edu/~rcarmona/

Discrete time competitive equilibrium models for cap-and-trade schemes and the clean development mechanism
June 10, 2010


Rene Carmona (Princeton University)
http://www.princeton.edu/~rcarmona/

Singular BSDEs appearing in cap-and-trade models
June 15, 2010


Rene Carmona (Princeton University)
http://www.princeton.edu/~rcarmona/

Game theory, Nash equilibrium, and electricity prices with strategic market players
June 16, 2010


Rene Carmona (Princeton University)
http://www.princeton.edu/~rcarmona/
Max Fehr (London School of Economics and Political Science)
http://www.ifor.math.ethz.ch/staff/maxfehr

Implementation of a simple model: second example
June 9, 2010


Rene Carmona (Princeton University)
http://www.princeton.edu/~rcarmona/

Stochastic games: Pontryagin maximum principle and the Isaacs conditions
June 17, 2010


Rene Carmona (Princeton University)
http://www.princeton.edu/~rcarmona/

Mathematical models for allocation mechanisms and cost distribution
June 9, 2010


Rene Carmona (Princeton University)
http://www.princeton.edu/~rcarmona/

Examples of linear-quadratic stochastic games in environmental finance
June 18, 2010


Rene Carmona (Princeton University)
http://www.princeton.edu/~rcarmona/

Energy and emissions markets, and the existing cap-and-trade schemes
June 7, 2010


Rene Carmona (Princeton University)
http://www.princeton.edu/~rcarmona/

Discrete time competitive equilibrium models for cap-and-trade schemes and the carbon tax
June 8, 2010


Ivar Ekeland (University of British Columbia)
http://www.pims.math.ca/~ekeland/

Non-constant discount rates, time inconsistency, and the golden rule
June 10, 2010

In economic theory one typically discounts future benefits at a constant rate. An example of this is the celebrated model of endogeneous growth, originating with Ramsey (1928), which leads to the so-called golden rule in macroeconomics. There are now excellent reasons (intergenerational equity, for instance) to use non-constant discount rates. There is then a problem of time-inconsistency: a policy which is optimal today will no longer be so when the time comes to implement it. So optimization is pointless, and a substitute has to be found for optimal strategies. We will define such a substitute, namely equilibrium strategies, show how to characterize them, and investigate what happens to the golden rule. This is joint work with Ali Lazrak.

Ivar Ekeland (University of British Columbia)
http://www.pims.math.ca/~ekeland/

The Merton problem with hyperbolic discounting
June 11, 2010

There is strong evidence that individuals discount future utilities at non-constant rates. The notion of optimality then disappears, because of time inconsistency (see the Tuesday colloquium) and rational behaviour then centers around equilibrium strategies. I will investigate portfolio management with hyperbolic discounting (the discount rate increases with time), and I will show that this may explain some well-known puzzles of portfolio management. This is joint work with Traian Pirvu.

Max Fehr (London School of Economics and Political Science)
http://www.ifor.math.ethz.ch/staff/maxfehr

Simulations of realistic EU ETS models
joint work with U. Cetin & P. Barrieu (London School of Economics)

June 7, 2010

We propose a model for risk neutral futures price dynamics in the European Unions Emissions Trading Scheme (EU ETS). Historical price dynamics suggests that both allowance prices for different compliance periods and CER prices for different compliance periods are significantly related. To obtain a realistic price dynamics we take into account the specific details of the EU ETS compliance regulations, such as banking and the link to the Clean Development Mechanism (CDM), and exploit arbitrage relationships between futures on EU allowances and Certified Emission Reductions.

Michael Ludkovski (University of California)
http://www.pstat.ucsb.edu/faculty/ludkovski/

Optimal switching problems and applications in energy finance
June 16, 2010

Optimal Switching models are concerned with sequential decision making where the controller has a finite number of policy regimes. Such models arise naturally in pricing of energy assets, including tolling agreements for electricity production, natural gas storage facilities, carbon emission permits, etc. I will discuss the general mathematical structure of optimal switching models, including their relation to multiple stopping problems. I will then describe some work in progress with R. Sircar on exploration control in exhaustible resource management.

In the second part of the talk, I will focus on numerical methods and implementation issues for optimal switching, especially simulation tools that extend Monte Carlo methods for American options.

Ronnie Sircar (Princeton University)
http://www.princeton.edu/~sircar/

Dynamic oligopolies and differential games. I
June 15, 2010

We discuss Cournot and Bertrand models of oligopolies, first in the context of static games and then in dynamic models. The static games, involving firms with different costs, lead to questions of how many competitors actively participate in a Nash equilibrium and how many are sidelined or blockaded from entry. The dynamic games lead to systems of nonlinear partial differential equations for which we discuss asymptotic and numerical approximations. Applications include competition between energy producers in the face of exhaustible resources such as oil (Cournot); and markets for substitutable consumer goods (Bertrand).

Ronnie Sircar (Princeton University)
http://www.princeton.edu/~sircar/

Dynamic oligopolies and differential games. II
June 17, 2010


Nizar Touzi (École Polytechnique)
http://www.cmap.polytechnique.fr/~touzi/

Backward stochastic differential equations and connection with semilinear PDEs
June 16, 2010


Nizar Touzi (École Polytechnique)
http://www.cmap.polytechnique.fr/~touzi/

Second order stochastic target problems
June 15, 2010


Nizar Touzi (École Polytechnique)
http://www.cmap.polytechnique.fr/~touzi/

Stochastic target problems and viscosity solutions
June 14, 2010


Nizar Touzi (École Polytechnique)
http://www.cmap.polytechnique.fr/~touzi/

Second order backward stochastic differential equations and connection with fully nonlinear PDEs
June 17, 2010


Nizar Touzi (École Polytechnique)
http://www.cmap.polytechnique.fr/~touzi/

Numerical methods for BSDEs and applications
June 18, 2010


Jianfeng Zhang (University of Southern California)
http://almaak.usc.edu/~jianfenz/

Martingale representation theorem for the G-expectation
June 14, 2010

In recent years Peng prososed a new notion called G-expectation, a type of nonlinear expectation motivated from dynamic risk measures with volatility uncertainty. On the other hand, a martingale under the G-expectation can be viewed as the solution to a "linear" Second Order Backward SDEs, the main subject of the short course which will be given by Nizar Touzi in this workshop. The theory has applications in many areas, e.g. Monte Carlo methods for fully nonlinear PDEs, finanancial problems in models with volatility uncertainty (volatility control, liquidity cost, Gamma constraint). Its main technical feature is the quasi-sure stochastic analysis, which invloves a class of mutually singular probability measures. In this talk we will introduce G-martingales, develop the quais-sure stochastic analysis, and establish the martingale epresentation theorem for G-martingales. This is a joint work with Mete Soner and Nizar Touzi.

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