Applied computational economics and finance.

*(English)*Zbl 1014.91015
Cambridge, MA: MIT Press. xviii, 510 p. (2002).

The book presents basics of numerical analysis of economic and financial models. The authors emphasize practical numerical methods, not mathematical proofs, and focus on techniques that are directly useful to economic analysts. The examples used in the book are drawn from a wide range of areas of economics and finance, with particular emphasis on problems in financial, agricultural, and resource economics as well as macroeconomics. Numerical methods and algorithms are illustrated using the computer language MATLAB. A toolbox of utilities, the CompEcon Toolbox, is provided to assist interested readers in developing their own computational economic applications.

The book is aimed at graduate students, advanced undergraduate students, and practicing economists.

The book is divided into two major parts. The first six chapters develop basic numerical methods, including linear and nonlinear equation methods, complimentary methods, finite-dimensional optimization, numerical integration and differentiation, and function approximation. An appreciation for basic numerical techniques is developed in these chapters by illustrating their application to equilibrium and optimization models familiar to most economists.

The second part consists of five chapters which are devoted to study dynamic economic and financial models. The first three chapters are devoted to the numerical analysis of dynamic models in discrete time and are followed by two chapters on dynamic models in continuous time. More specifically, Chapter 7 study the simplest of these models: the discrete time, discrete state Markov decision model. Chapters 8 and 9 study those discrete time dynamic models whose state variables may assume a continuum values. Chapters 10 and 11 are devoted to models which treat time as a continuum. In particular, the authors discuss models of asset prices that are based on arbitrage considerations alone and that do not depend on solving a decision problem. Many financial assets, including bonds, futures, and some options are in this class.

After that the authors discuss the topic of stochastic control divided into three subtypes. The first, continuous-action problems, having a control that can take any value on a continuum. For the second subtype, discrete-action problems, the control is a choice among a set of discrete states. The third, impulse control, comprises problems for which the optimal control can be extended at an infinite rate, causing a discrete jump in the value of state variable. Since continuous-time economic models result in economic processes that satisfy differential equations, the last chapter is devoted for numeric methods of solving partial differential equations. The authors concentrate on an approach that encompasses a number of the more common methods. Specifically, the true but unknown solution is replaced with a convenient approximating function, the parameters of which are determined using collocation. For initial value problems, this approach is combined with a recursive algorithm. The authors also discuss free-boundary problems that arise in some control problems.

According to the authors, no attempt was made to be encyclopedic in their coverage of numerical methods or potential applications. Instead, a relatively small number of techniques was chosen to develop and apply to a wide variety of economic problems. In some instances, the authors deviated from the standard treatments of numerical methods in existing textbooks in order to present a simple, consistent framework that may be readily learned and applied by economists. A certain numerical technique was not covered in those cases when it was considered to be of limited benefit to economists, relative to their complexity. However, throughout the book the authors explain their choices and give references to more advanced numerical textbooks where appropriate.

The book is aimed at graduate students, advanced undergraduate students, and practicing economists.

The book is divided into two major parts. The first six chapters develop basic numerical methods, including linear and nonlinear equation methods, complimentary methods, finite-dimensional optimization, numerical integration and differentiation, and function approximation. An appreciation for basic numerical techniques is developed in these chapters by illustrating their application to equilibrium and optimization models familiar to most economists.

The second part consists of five chapters which are devoted to study dynamic economic and financial models. The first three chapters are devoted to the numerical analysis of dynamic models in discrete time and are followed by two chapters on dynamic models in continuous time. More specifically, Chapter 7 study the simplest of these models: the discrete time, discrete state Markov decision model. Chapters 8 and 9 study those discrete time dynamic models whose state variables may assume a continuum values. Chapters 10 and 11 are devoted to models which treat time as a continuum. In particular, the authors discuss models of asset prices that are based on arbitrage considerations alone and that do not depend on solving a decision problem. Many financial assets, including bonds, futures, and some options are in this class.

After that the authors discuss the topic of stochastic control divided into three subtypes. The first, continuous-action problems, having a control that can take any value on a continuum. For the second subtype, discrete-action problems, the control is a choice among a set of discrete states. The third, impulse control, comprises problems for which the optimal control can be extended at an infinite rate, causing a discrete jump in the value of state variable. Since continuous-time economic models result in economic processes that satisfy differential equations, the last chapter is devoted for numeric methods of solving partial differential equations. The authors concentrate on an approach that encompasses a number of the more common methods. Specifically, the true but unknown solution is replaced with a convenient approximating function, the parameters of which are determined using collocation. For initial value problems, this approach is combined with a recursive algorithm. The authors also discuss free-boundary problems that arise in some control problems.

According to the authors, no attempt was made to be encyclopedic in their coverage of numerical methods or potential applications. Instead, a relatively small number of techniques was chosen to develop and apply to a wide variety of economic problems. In some instances, the authors deviated from the standard treatments of numerical methods in existing textbooks in order to present a simple, consistent framework that may be readily learned and applied by economists. A certain numerical technique was not covered in those cases when it was considered to be of limited benefit to economists, relative to their complexity. However, throughout the book the authors explain their choices and give references to more advanced numerical textbooks where appropriate.

Reviewer: Rimas Norvaiša (Vilnius)

##### MSC:

91B02 | Fundamental topics (basic mathematics, methodology; applicable to economics in general) |

65-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis |

91-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance |