Creative Commons Attribution-ShareAlike 4.0 International
This œuvre, An Information Geometry Problem in Mathematical Finance, by Michel Broniatowski is licensed under a Creative Commons Attribution-ShareAlike 4.0 International license.

An Information Geometry Problem in Mathematical Finance


An Information Geometry Problem in Mathematical Finance
Publication details: 
Familiar approaches to risk and preferences involve minimizing the expectation EIP(X) of a payoff function X over a family Γ of plausible risk factor distributions IP. We consider Γ determined by a bound on a convex integral functional of the density of IP, thus Γ may be an I-divergence (relative entropy) ball or some other f-divergence ball or Bregman distance ball around a default distribution IPo. Using a Pythagorean identity we show that whether or not a worst case distribution exists (minimizing EIP(X) subject to IP∈Γ), the almost worst case distributions cluster around an explicitly specified, perhaps incomplete distribution. When Γ is an f-divergence ball, a worst case distribution either exists for any radius, or it does/does not exist for radius less/larger than a critical value. It remains open how far the latter result extends beyond f-divergence balls.
Source et DOI
An Information Geometry Problem in Mathematical Finance
Groupes / audience: