Convexity and Optimization in Finite Dimensions I

TL;DR: In this paper, the authors considered systems of partial differential equations with only second derivatives in the x variables and which are uniformly parabolic in the sense of Petrovskii and obtained necessary and sufficient conditions for the maximum norm principle to hold in the layer Rn × (0,T ) and in the cylinder Ω × ( 0,T], where Ω is a bounded subdomain of Rn.

TL;DR: In this paper, the numerical solution of the Black-Scholes equation for European plain-vanilla options, and of the corresponding inequalities for the American-style case, are described and compared.

TL;DR: It is surveyed three ways to multiply elements of the additive subgroup of the group of real-valued functions on Rd which is generated by the indicator functions of polyhedra, including Ehrhart polynomials, mixed volumes, Gram’s relation, and transversal characteristics.

TL;DR: The marked representation theorem for lineally closed convex sets without lines was established in this paper, in which every point of C can be represented in unique way as a convex (nonnegative) linear combination of points (directions) of C which are independent, and this representation can be determined by an algorithm of successive extractions.