John Armstrong

Local Rigidity of Certain Classes of Almost Kähler 4-Manifolds

We show that any non-Kähler, almost Kähler 4-manifoldfor which both the Ricci and the Weyl curvatures have the same algebraic symmetries as they have for a Kähler metric is locally isometric to the (only)proper 3-symmetric four-dimensional space.

Symplectic 4-manifolds with Hermitian Weyl tensor

It is proved that any compact almost Kihler, Einstein 4-manifold whose fundamental form is a root of the Weyl tensor is necessarily Kihler.

Small-time asymptotics for a general local-stochastic volatility model with a jump-to-default: curvature and the heat kernel expansion

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 expansion combined with Laplaces method to integrate over the volatility variable on a compact set, and (after a gauge transformation) we use the Davies \cite{Dav88} upper bound for the heat kernel on a manifold with bounded Ricci curvature to deal with the tail integrals. If the correlation

Extrinsic Projection of Itô SDEs on Submanifolds with Applications to Non-linear Filtering

\rho 0

Small-Time Asymptotics under Local-Stochastic Volatility with a Jump-to-Default: Curvature and the Heat Kernel Expansion

, the implied volatility increases by

Twistor Topology of the Fermat Cubic

\lm f(x) t +o(t)

The Pontryagin Forms of Hessian Manifolds

for some function

Stochastic filtering by projection: The example of the quadratic sensor

f(x)

Intrinsic stochastic differential equations as jets

which blows up as

Itô Stochastic Differential Equations as 2-Jets

x \searrow 0