Math notes to write up - Adam Oberman Math

Math notes to write up

Contents

Arbitrage: write out the parable of the bookie

  • This is in the introduction to Duffie book.


Voronoi Diagram and Delaunay Triangulation

  • Show that these are dual objects, and that they can be found using the Convex Hull of the lift onto a parabola. Then by taking the Legendre Transform.

Lipschitz extensions of functions

  • Review the McShane and Whitney extensions (pictures from my IL article in Proc AMS)
  • Explain my extension which preserves the maximum principle
  • mention the optimal extensions, and the Aronsson equation, and cite Mike Crandall Tour from Bulletin of the AMS.

Stochastic Inventory

  • The story of the paperboy, optimal invetory given stochastic demand (first page of the book)

Gamma convergence applied to homgenization

  • First couple of pages of the notes