Minicourse: Equilibrium Analysis and Variational Convergence

Lecturer: Roger Wets (UC Davis)

 

Organised by Deutsche Bank Chair - Applied Financial Mathematics - Ulrich Horst.

 

Predominant theme: Dealing with equilibrium problems, mostly as they arise in microeconomics, but from a somewhat more comprehensive mathematical viewpoint: (variational) analysis, approximation and computational schemes. The third lecture is devoted to a variant of the 'standard' equilibrium model with incomplete financial markets.

• Lecture 1. Variational Convergence: Univariate Case
  • review of set convergence
  • epi-convergence: definition, main implications, epi-tight property
  • epi-convergence and convexity, equi-lower semicontinuity
  • metrization, the epi-topology; hypo-convergence
• Lecture 2. Variationl Convergence: Bivariate Case
• epi/hypo-convergence of saddle functions & applications
• lopsided (or lop-)convergence of bivariate functions, properties
• non-cooperative games, variational inequalities and equilibrium problems
• Lecture 3. A GEI time-dependent model
  • the static Arrow-Debreu model
  • Keynes prescriptions, time-dependent model: real assets
  • the value of money
  • completed equilibrium, variational modeling of equilibrium
• Lecture 4. Finding solutions to equilibrium problems
  • relationship between equilibrium and other variational problems
  • static and dynamic (deterministic) equilibrium problems
  • strategy based on finding maxinf points of bivariate functions
  • strategy based on solving the associated Variational Inequality
  • dealing with equilibrium problems in a stochastic environment

The first course takes place on Wednesday, May 5th, 11.30 a.m., room 1.013, Rudower Chaussee 25.