Abstract Discrete duality finite volume (DDFV) schemes are known for their ability to approximate nonlinear and linear anisotropic diffusion operators on general meshes, but they possess several drawbacks. The most important drawback of DDFV is the simultaneous use cell node unknowns. We propose a discretization approach that incorporates ideas associated analysis techniques, allows rapid elimi...

This chapter describes how duality and approximate dynamic programming (ADP) methods can be used in financial engineering. It focuses on American option pricing and portfolio optimization problems when the underlying state space is high-dimensional. In general, it is not possible to solve these problems exactly due to the so-called “curse of dimensionality” and as a result, approximate solution...

This chapter describes how duality and approximate dynamic programming (ADP) methods can be used in financial engineering. It focuses on American option pricing and portfolio optimization problems when the underlying state space is highdimensional. In general, it is not possible to solve these problems exactly due to the so-called “curse of dimensionality” and as a result, approximate solution ...

The regularization path of the Lasso can be shown to be piecewise linear, making it possible to “follow” and explicitly compute the entire path. We analyze in this paper this popular strategy, and prove that its worst case complexity is exponential in the number of variables. We then oppose this pessimistic result to an (optimistic) approximate analysis: We show that an approximate path with at...

This paper presents a brief introduction to the use of duality theory and simulation in financial engineering. It focuses on American option pricing and portfolio optimization problems when the underlying state space is high-dimensional. In general, it is not possible to solve these problems exactly due to the so-called “curse of dimensionality” and as a result, approximate solution techniques ...

Duality for robust hedging with proportional transaction costs of path dependent European options is obtained in a discrete time financial market with one risky asset. Investor’s portfolio consists of a dynamically traded stock and a static position in vanilla options which can be exercised at maturity. Only stock trading is subject to proportional transaction costs. The main theorem is duality...

We consider the problem of producing lower bounds on the optimal cost-to-go function of a Markov decision problem. We present two approaches to this problem: one based on the methodology of approximate linear programming (ALP) and another based on the so-called martingale duality approach. We show that these two approaches are intimately connected. Exploring this connection leads us to the prob...

Limit analysis studies the asymptotic behavior of elastic-plastic materials and structures. The asymptotic material properties exist for a class of ductile metals and are designed into optimal structural members such as I-beams and composite plates. The analysis automatically ignores the relatively small elastic deformations. Classical lower and upper bound theorems in the form of inequalities ...

We present a recent determination of an approximate expression for the O(α3s) contribution χ2 to the kernel of the BFKL equation. This includes all collinear and anticollinear singular contributions and is derived using duality relations between the GLAP and BFKL kernels. † Talk presented at 12 International Conference on Elastic and Diffractive Scattering: Forward Physics and QCD, DESY, Hambur...