26 citations · 77 across the 19 of their papers we have counts for
4 papers · 1 filter
Curvature of Hessian Manfiolds
Shun-ichi Amari, John Armstrong
We prove that, in dimensions greater than 2, the generic metric is not a Hessian metric and find a curvature condition on Hessian metrics in dimensions greater than 3. In particula…
Small-time asymptotics for a general local-stochastic volatility model with a jump-to-default: curvature and the heat kernel expansion
John Armstrong, Martin Forde, Matthew Lorig +1
We compute a sharp small-time estimate for implied volatility under a general uncorrelated local-stochastic volatility model. For this we use the Bellaiche \cite{Bel81} heat kernel…
Twistor Topology of the Fermat Cubic
John Armstrong, Simon Salamon
We describe topologically the discriminant locus of a smooth cubic surface in the complex projective space that contains 5 fibres of the projection ${\mathbb{CP}}…
Stochastic filtering via L2 projection on mixture manifolds with computer algorithms and numerical examples
John Armstrong, Damiano Brigo
We examine some differential geometric approaches to finding approximate solutions to the continuous time nonlinear filtering problem. Our primary focus is a new projection method…