Optimal investment L.C.G. Rogers

Format:

Book

Author/Creator:

Rogers, L. C. G.

Series:

SpringerBriefs in quantitative finance

SpringerBriefs in quantitative finance 2192-7006

Language:

English

Subjects (All):

Investment analysis--Mathematical models.

Investment analysis.

Merton Model.

Investments.

Mathematics.

Quantitative Finance.

Finance, general.

Numerical Analysis.

Calculus of Variations and Optimal Control; Optimization.

Probability Theory and Stochastic Processes.

Medical Subjects:

Investments.

Local Subjects:

Mathematics.

Quantitative Finance.

Finance, general.

Numerical Analysis.

Calculus of Variations and Optimal Control; Optimization.

Probability Theory and Stochastic Processes.

Physical Description:

1 online resource

Place of Publication:

Berlin New York Springer ©2013

Language Note:

English

System Details:

PDF

text file

Summary:

Readers of this book will learn how to solve a wide range of optimal investment problems arising in finance and economics. Starting from the fundamental Merton problem, many variants are presented and solved, often using numerical techniques that the book also covers. The final chapter assesses the relevance of many of the models in common use when applied to data

Contents:

1. The Merton Problem Introduction The Value Function Approach The Dual Value Function Approach The Static Programming Approach The Pontryagin-Lagrange Approach When is the Merton Problem Well Posed? Linking Optimal Solutions to the State-Price Density Dynamic Stochastic General Equilibrium Models CRRA Utility and Efficiency

2. Variations The Finite-Horizon Merton Problem Interest-Rate Risk A Habit Formation Model Transaction Costs Optimisation under Drawdown Constraints Annual Tax Accounting History-Dependent Preferences Non-CRRA Utilities An Insurance Example with Choice of Premium Level Markov-Modulated Asset Dynamics Random Lifetime Random Growth Rate Utility from Wealth and Consumption Wealth Preservation Constraint Constraint on Drawdown of Consumption Option to Stop Early Optimization under Expected Shortfall Constraint Recursive Utility Keeping up with the Jones's Performance Relative to a Benchmark Utility from Slice of the Cake Investment Penalized by Riskiness Lower Bound for Utility Production and Consumption Preferences with Limited Look-Ahead Investing in an Asset with Stochastic Volatility Varying Growth Rate Beating a Benchmark Leverage Bound on the Portfolio Soft Wealth Drawdown Investment with Retirement Parameter Uncertainty Robust Optimization Labour Income

3. Numerical Solution Policy Improvement Optimal Stopping One-Dimensional Elliptic Problems Multi-Dimensional Elliptic Problems Parabolic Problems Boundary Conditions Iterative Solutions of PDEs Policy Improvement Value Recursion Newton's Method

4. How Well Does It Work? Stylized Facts About Asset Returns Estimation of l: The 20s Example Estimation of V.

Machine generated contents note: 1. Merton Problem

1.1. Introduction

1.2. Value Function Approach

1.3. Dual Value Function Approach

1.4. Static Programming Approach

1.5. Pontryagin-Lagrange Approach

1.6. When is the Merton Problem Well Posed

1.7. Linking Optimal Solutions to the State-Price Density

1.8. Dynamic Stochastic General Equilibrium Models

1.9. CRRA Utility and Efficiency

2. Variations

2.1. Finite-Horizon Merton Problem

2.2. Interest-Rate Risk

2.3. Habit Formation Model

2.4. Transaction Costs

2.5. Optimisation under Drawdown Constraints

2.6. Annual Tax Accounting

2.7. History-Dependent Preferences

2.8. Non-CRRA Utilities

2.9. Insurance Example with Choice of Premium Level

2.10. Markov-Modulated Asset Dynamics

2.11. Random Lifetime

2.12. Random Growth Rate

2.13. Utility from Wealth and Consumption

2.14. Wealth Preservation Constraint

2.15. Constraint on Drawdown of Consumption

2.16. Option to Stop Early

2.17. Optimization under Expected Shortfall Constraint

2.18. Recursive Utility

2.19. Keeping up with the Jones's

2.20. Performance Relative to a Benchmark

2.21. Utility from Slice of the Cake

2.22. Investment Penalized by Riskiness

2.23. Lower Bound for Utility

2.24. Production and Consumption

2.25. Preferences with Limited Look-Ahead

2.26. Investing in an Asset with Stochastic Volatility

2.27. Varying Growth Rate

2.28. Beating a Benchmark

2.29. Leverage Bound on the Portfolio

2.30. Soft Wealth Drawdown

2.31. Investment with Retirement

2.32. Parameter Uncertainty

2.33. Robust Optimization

2.34. Labour Income

3. Numerical Solution

3.1. Policy Improvement

3.1.1. Optimal Stopping

3.2. One-Dimensional Elliptic Problems

3.3. Multi-Dimensional Elliptic Problems

3.4. Parabolic Problems

3.5. Boundary Conditions

3.6. Iterative Solutions of PDEs

3.6.1. Policy Improvement

3.6.2. Value Recursion

3.6.3. Newton's Method

4. How Well Does It Work

4.1. Stylized Facts About Asset Returns

4.2. Estimation of μ The 20s Example

4.3. Estimation of V.

Notes:

Includes bibliographical references and index

Other Format:

Print version Rogers, L.C.G. Optimal Investment

ISBN:

9783642352027

3642352022

3642352014

9783642352010

1299197892

9781299197893

OCLC:

824936095

Access Restriction:

Restricted for use by site license