Impulse Control and Quasi-variational Inequalities
Impulse Control and Quasi-variational Inequalities

Author: Alain Bensoussan

Publisher: Bordas Editions

Published: 1984

Total Pages: 712

ISBN-13:

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"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.

Applied Stochastic Control of Jump Diffusions
Applied Stochastic Control of Jump Diffusions

Author: Bernt Øksendal

Publisher: Springer

Published: 2019-04-17

Total Pages: 439

ISBN-13: 3030027813

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Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

Deterministic and Stochastic Optimal Control and Inverse Problems
Deterministic and Stochastic Optimal Control and Inverse Problems

Author: Baasansuren Jadamba

Publisher: CRC Press

Published: 2021-12-15

Total Pages: 378

ISBN-13: 1000511758

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Inverse problems of identifying parameters and initial/boundary conditions in deterministic and stochastic partial differential equations constitute a vibrant and emerging research area that has found numerous applications. A related problem of paramount importance is the optimal control problem for stochastic differential equations. This edited volume comprises invited contributions from world-renowned researchers in the subject of control and inverse problems. There are several contributions on optimal control and inverse problems covering different aspects of the theory, numerical methods, and applications. Besides a unified presentation of the most recent and relevant developments, this volume also presents some survey articles to make the material self-contained. To maintain the highest level of scientific quality, all manuscripts have been thoroughly reviewed.

Applied Stochastic Control of Jump Diffusions
Applied Stochastic Control of Jump Diffusions

Author: Bernt Øksendal

Publisher: Springer

Published: 2009-09-02

Total Pages: 262

ISBN-13: 9783540834861

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Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

OPTIMAL CONTROL, DIFFERENTIAL VARIATIONAL INEQUALITIES, AND THEIR APPLICATION TO TRAFFIC SCIENCE, REVENUE MANAGEMENT AND SUPPLY CHAINS.
OPTIMAL CONTROL, DIFFERENTIAL VARIATIONAL INEQUALITIES, AND THEIR APPLICATION TO TRAFFIC SCIENCE, REVENUE MANAGEMENT AND SUPPLY CHAINS.

Author: Yiou Wang

Publisher:

Published: 2018

Total Pages:

ISBN-13:

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Optimal control problems and differential Nash games have been employed by many scholars in the study of dynamic pricing, supply chain management and transportation network flow problems. This dissertation emphasizes the extensionof frequently employed deterministic, open-loop modeling paradigms into feedback and stochastic cases respectively with a focus on the computational perspective.For the feedback differential Nash games, this dissertation briefly reviews the classical theory of Hamilton-Jacobi-Bellman equation and the general technique to synthesis feedback optimal control from its solution. Such techniques are then applied to the investigation of a dynamic competitive pricing problem of perishable products with fixed initial inventories (DPFI). Other qualitative analysis and numerical extensions of the DPFI model are also provided.In the study of differential Nash games with Ito-type of stochastic dynamics, this dissertation starts from reviewing the stochastic maximum principle. It then proposes stochastic differential variational inequality (S-DVI) as the necessary condition for stochastic differential Nash games. As an application, this dissertation provides formulation, qualitative analysis and algorithm for a stochastic differential oligopsony problem where multiple agents compete in the procurement of key rawmaterial which follows Ito-type of stochastic price dynamics.

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

Published: 2012-12-06

Total Pages: 275

ISBN-13: 1461220688

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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.