Foto del docente

Enrico Bernardi

Professor

Department of Statistical Sciences "Paolo Fortunati"

Academic discipline: MAT/05 Mathematical Analysis

Research

Keywords: Hyperbolic Equations Gevrey Classes Cauchy Problem Stochastic differential equations Quantitative Finance

1) Cauchy Problem for linear hyperbolic operators with multiple characteristics.
2) Gevrey regularity and propagation of singularities for weakly hyperbolic psuedo-differential eqautions.
3) Stochastic Hamiltonian Problems.

For the Hyperbolic Cauchy Problem with double characteristics in recent papers with T.Nishitani we have come to the complete understanding of the geometric interplay of the linear algebraic classification of symplectic matrices at multiple points and the stability of the geometry ot the curves which are soultions of the Hamiltonian system naturally associated with the principal symbol of the operator examined.
It has been a problem which only recently can be declared to be solved the fact that when the fundamental matrix has a Jordan block of size bigger than 2 in its canonical decomposition new instabilities tend to appear and can interact with lower order terms in the classical development of the symbol.

We study numerical methods for systems of Hamiltonian stochastic equations with non Lipschitz coefficients originating from quantitative finance problems.


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