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This paper is devoted to the derivation of some regularity properties of pricing functions for American options and to the discussion of numerical methods, based on the Bensoussan-Lions methods of variational inequalities. In particular, we provide a complete justification of the so-called...
A symmetrizer of the matrix A is a symmetric solution X that satisfies the matrix equation XA=A′X. An exact matrix symmetrizer is computed by obtaining a general algorithm and superimposing a modified multiple modulus residue arithmetic on this algorithm. A procedure based on computing a...
We discuss an explicit example of a map of the plane R
2 with a nontrivial attracting set. In particular, we are concerned with the concept of rotation number introduced by Poincaré for maps of the circle and its subsequent extension by Birkhoff to maps of the annulus. The use of rotation number...
The existence of global generalized solutions is proved for arbitrary analytic nonlinear PDEs on the whole of their domains of analyticity. The solutions are analytic outside of closed, nowhere dense subsets.
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