Stochastic economic dynamics / Bjarne S. Jensen & Tapio Palokangas (editors).

Format:

Book

Contributor:

Jensen, Bjarne S.

Palokangas, Tapio.

Language:

English

Subjects (All):

Stochastic processes.

Statics and dynamics (Social sciences).

Physical Description:

438 p. : ill.

Edition:

1st ed.

Place of Publication:

[Copenhagen?] : Copenhagen Business School Press ; Portland, OR : International Specialized Book Services [distributor], c2007.

Language Note:

English

Summary:

This book analyzes stochastic dynamic systems across a broad spectrum in economics and finance. The major unifying theme is the coherent and rigorous treatment of uncertainty and its implications for describing stochastic processes by the stochastic differential equations of the fundamental models in various fields. Pertinent subjects are interrelated, juxtaposed, and examined for consistency in theoretical and empirical contexts. The volume consists of three parts: Developments in Stochastic Dynamics; Stochastic Dynamics in Basic Economic Growth Models; and Intertemporal Optimization in Consumption, Finance, and Growth. Key topics include: fractional Brownian motion in finance; moment evolution of Gaussian and geometric Wiener diffusions; stochastic kinematics and stochastic mechanics; stochastic growth in continuous time; time delays and Hopf bifurcation; consumption and investment strategies; differential systems in finance and life insurance; uncertainty of technological innovations; investment and employment cycles; stochastic control theory; and risk aversion. The works collected in this book serves to bridge the "old" deterministic dynamics and the "new" stochastic dynamics. The collection is important for scholars and advanced graduate students of economics, statistics, and applied mathematics.

Contents:

Stochastic Economic Dynamics

Table of Contents

Introduction

Part I: Developments in Stochastic Dynamics

1. Fractional Brownian Motion in Finance

1.1 Introduction

1.2 Framework and definitions

1.3 Classical white noise theory and Hida-Malliavin calculus

1.4 Fractional stochastic calculus

1.5 Summary of results

1.6 Concluding remarks

2. Moment Evolution of Gaussian and Geometric Wiener Diffusions

2.1 Introduction

2.2 Structure of basic diffusion processes

2.3 Dynamics of first-order and second-order moments

2.4 Expectation vector functions

2.5 Covariance matrix functions

2.6 Probability density functions

2.7 Final comments

Appendices

3. Two-Dimensional Linear Dynamic Systems with Small Random Terms

3.1 Introduction

3.2 Non-random dynamic system

3.3 Lyapunov index of the random system

3.4 One-dimensional diffusion process in an interval

3.5 Spiral point and center

3.6 Saddle point

3.7 Improper and proper node

4. Dynamic Theory of Stochastic Movement of Systems

4.1 Dynamic theory of stochastic processes

4.2 Kinematic theory

4.3 Sample path equation in kinematic theory

4.4 Mechanics and the equation of motion

4.5 Evolution function and kinematic equation

4.6 Exponent of motion and initial condition

4.7 Examples

4.8 Schr¨odinger's wave theory and dynamic theory

4.9 Sample paths of motion governed by theSchr¨odinger equation

4.10 Interference phenomena and entangled motion

Part II: Stochastic Dynamics of BasicGrowth Models and Time Delays

5. Stochastic One-Sector and Two-Sector Growth Models in Continuous Time

5.1 Introduction

5.2 Neoclassical technologies and CES forms

5.3 Stochastic one-sector growth models

5.4 Boundaries, steady-state, and convergence

5.5 Explicit steady-state distribution with CD technologies.

5.6 Sample paths and asymptotic densities with CD andCES technologies

5.7 General equilibria of two-sector economies

5.8 Dynamics of two-sector economies

5.9 Sample paths of two-sector models and CES

6. Comparative Dynamics in a Stochastic Growth and Trade Model with a Variable Savings Rate

6.1 Introduction

6.2 Stochastic dynamic systems for trading economies

6.3 Comparative dynamics and policy parameters

7. Inada Conditions and Global Dynamic Analysis of Basic Growth Models with Time Delays

7.1 Introduction

7.2 Neoclassical growth model with time delays

7.3 Dynamics with delays in production and depreciation

7.4 Persistent oscillation in a growth model with delays

7.5 Final comments

8. Hopf Bifurcation in Growth Models with Time Delays

8.1 Introduction

8.2 Dynamics of growth and cycles

8.3 Hopf bifurcation analysis

8.4 CD technologies and time delays

8.5 CES technologies and time delays

8.6 CES and delays with cycles, square waves, and chaos

8.7 Final comments

Part III: Intertemporal Optimization in Consumption, Finance, and Growth

9. Optimal Consumption and Investment Strategiesin Dynamic Stochastic Economies

9.1 Introduction

9.2 Consumption and investment in complete markets

9.3 Results for CRRA utility in general markets

9.4 Examples

9.5 Extensions

9.6 Concluding remarks

Appendix

10. Differential Systems in Finance and Life Insurance

10.1 Introduction

10.2 The differential equations of Thiele and Black-Scholes

10.3 Surplus and dividends

10.4 Intervention

10.5 Quadratic optimization

10.6 Utility optimization

11. Uncertain Technological Change and Capital Mobility

11.1 Introduction

11.2 Framework of the model

11.3 The effect of uncertainty on growth

11.4 Conclusion

Appendices.

12. Stochastic Control, Non-Depletion of Renewable Resources, and Intertemporal Substitution

12.1 Introduction

12.2 The preferences

12.3 The optimal control problem

12.4 Non-optimality of immediate total depletion

12.5 Concluding remarks

13. Capital Accumulation in a Growth Model with Creative Destruction

13.1 Introduction

13.2 Framework of the model

13.3 Solving the model

13.4 Cycles and growth

13.5 Conclusions

14. Employment Cycles in a Growth Model with Creative Destruction

14.1 Introduction

14.2 Technology

14.3 R&amp

D and capital accumulation

14.4 Capitalists

14.5 Wage settlement

14.6 Economic growth

14.7 Cycles

14.8 Conclusions.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references.

ISBN:

87-630-9982-9

OCLC:

769114323