Ping Chen, Sardar Islam - Optimal Control Models in Finance. A New Computational Approach:
This book reports initial efforts in providing some useful extensions in - financial modeling; further work is necessary to complete the research agenda. The demonstrated extensions in this book in the computation and modeling of optimal control in finance have shown the need and potential for further areas of study in financial modeling. Potentials are in both the mathematical structure and computational aspects of dynamic optimization. There are needs for more organized and coordinated computational approaches. These extensions will make dynamic financial optimization models relatively more stable for applications to academic and practical exercises in the areas of financial optimization, forecasting, planning and optimal social choice.
This book will be useful to graduate students and academics in finance, mathematical economics, operations research and computer science. Professional practitioners in the above areas will find the book interesting and informative. The authors thank Professor B.D. Craven for providing extensive guidance and assistance in undertaking this research.
This work owes significantly to him, which will be evident throughout the whole book. The differential eq- tion solver “nqq” used in this book was first developed by Professor Craven. Editorial assistance provided by Matthew Clarke, Margarita Kumnick and Tom Lun is also highly appreciated. Ping Chen also wants to thank her parents for their constant support and love during the past four years.
Review
"This book by Ping Chen and Sardar M. N. Islam discusses the issue of the determination of optimal capital structure for corporations and the economy. They have developed an optimal control model for optimal financing involving a dynamic system with switching times. A new computational method and a new computer program named CSTVA are developed and optimal financing implications of the model results are analyzed in this book. This book makes a significant contribution to the literature and will surely prove to be a boon to students, academics, and practitioners in finance, optimal control, and computer programming.”
―Professor David W. K. Yeung, Professor of Decision Sciences, Hong Kong Baptist University, Director of Center of Game Theory, and Managing Editor, International Game Theory Review
From the Back Cover
The determination of optimal financing and investment strategies (optimal capital structure or optimal mix of funds, optimal portfolio choice, etc.) for corporations and the economy are important for efficient allocation of resources in the economy. Optimal control methods have useful applications to these areas in finance - some optimization problems in finance include optimal control, involving a dynamic system with switching times in the form of bang-bang control. Optimal control models for corporate finance and the economy are presented in this book and the analytical and computational results of these models are also reported. Such computational approaches to the study of optimal corporate financing are not well known in the existing literature.
This book develops a new computational method where switching times are considered as variables in the optimal dynamic financial model represented by a second-order differential equation. A new computer program named CSTVA (Computer Program for the Switching Time Variables Algorithm), which can compute bang-bang optimal financial models with switching time, is also developed. Optimal financing implications of the model results in the form of optimal switching times for changes in financing policies and the optimal financial policies are analyzed.
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