Optional decomposition and Lagrange multipliers

Optional decomposition and Lagrange multipliers

Let Q be the set of equivalent martingale measures for a given process S, and let X be a process which is a local supermartingale with respect to any measure in Q. The optional decomposition theorem for X states that there exists a predictable integrand φ such that the difference X−φ ·S is a decreasing process. In this paper we give a new proof which uses techniques from stochastic calculus rat...

Domain Decomposition with Lagrange Multipliers

Lagrange Multipliers and Optimality

Lagrange multipliers used to be viewed as auxiliary variables introduced in a problem of constrained minimization in order to write first-order optimality conditions formally as a system of equations. Modern applications, with their emphasis on numerical methods and more complicated side conditions than equations, have demanded deeper understanding of the concept and how it fits into a larger t...

Substructuring by Lagrange Multipliers

Dynamic Programming and Lagrange Multipliers.