Impulse Control and Quasi-variational Inequalities

Impulse Control and Quasi-variational Inequalities
Author: Alain Bensoussan
Publisher: Bordas Editions
Total Pages: 712
Release: 1984
Genre: Calculus of variations
ISBN:

"The general aim of this book is to establish and study the relations that exist, via dynamic programming, between, on the one hand, stochastic control, and on the other hand variational and quasi-variational inequalities, with the intention of obtaining constructive methods of solution by numerical methods. It begins with numerous examples which occur in applications and goes on to study, from an analytical viewpoint, both elliptic and parabolic quasi-variational inequalities. Finally the authors reconstruct an optimal control starting from the solution of the quasi-variational inequality."--Amazon.

A Stochastic Control Framework for Real Options in Strategic Evaluation

A Stochastic Control Framework for Real Options in Strategic Evaluation
Author: Alexander Vollert
Publisher: Springer Science & Business Media
Total Pages: 275
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461220688

The theoretical foundation for real options goes back to the mid 1980s and the development of a model that forms the basis for many current applications of real option theory. Over the last decade the theory has rapidly expanded and become enriched thanks to increasing research activity. Modern real option theory may be used for the valuation of entire companies as well as for particular investment projects in the presence of uncertainty. As such, the theory of real options can serve as a tool for more practically oriented decision making, providing management with strategies maximizing its capital market value. This book is devoted to examining a new framework for classifying real options from a management and a valuation perspective, giving the advantages and disadvantages of the real option approach. Impulse control theory and the theory of optimal stopping combined with methods of mathematical finance are used to construct arbitrarily complex real option models which can be solved numerically and which yield optimal capital market strategies and values. Various examples are given to demonstrate the potential of this framework. This work will benefit the financial community, companies, as well as academics in mathematical finance by providing an important extension of real option research from both a theoretical and practical point of view.

A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling

A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling
Author: Jörg Steinbach
Publisher: Birkhäuser
Total Pages: 297
Release: 2012-12-06
Genre: Mathematics
ISBN: 3034875975

This monograph studies an evolutionary variational inequality approach to a degenerate moving free boundary problem. It takes an intermediate position between elliptic and parabolic inequalities and comprises an elliptic differential operator, a memory term and time-dependent convex constraint sets. Finally, a description of injection and compression moulding is presented in terms of different mathematical models, a generalized Hele-Shaw flow, a distance concept and Navier-Stokes flow.

Mathematical Programs with Equilibrium Constraints

Mathematical Programs with Equilibrium Constraints
Author: Zhi-Quan Luo
Publisher: Cambridge University Press
Total Pages: 432
Release: 1996-11-13
Genre: Mathematics
ISBN: 9780521572903

An extensive study for an important class of constrained optimisation problems known as Mathematical Programs with Equilibrium Constraints.

Variational Analysis

Variational Analysis
Author: R. Tyrrell Rockafellar
Publisher: Springer Science & Business Media
Total Pages: 747
Release: 2009-06-26
Genre: Mathematics
ISBN: 3642024319

From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.

Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations

Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations
Author: Martino Bardi
Publisher: Springer Science & Business Media
Total Pages: 588
Release: 2009-05-21
Genre: Science
ISBN: 0817647554

This softcover book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton–Jacobi type and its interplay with Bellman’s dynamic programming approach to optimal control and differential games. It will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book.

Paris-Princeton Lectures on Mathematical Finance 2010

Paris-Princeton Lectures on Mathematical Finance 2010
Author: Areski Cousin
Publisher: Springer Science & Business Media
Total Pages: 374
Release: 2011-06-29
Genre: Mathematics
ISBN: 3642146597

The Paris-Princeton Lectures in Financial Mathematics, of which this is the fourth volume, publish cutting-edge research in self-contained, expository articles from outstanding specialists - established or on the rise! The aim is to produce a series of articles that can serve as an introductory reference source for research in the field. The articles are the result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with five articles by: 1. Areski Cousin, Monique Jeanblanc and Jean-Paul Laurent, 2. Stéphane Crépey, 3. Olivier Guéant, Jean-Michel Lasry and Pierre-Louis Lions, 4. David Hobson and 5. Peter Tankov.