Title Optimal investment / L.C.G. Rogers

Published Berlin ; New York : Springer, ©2013

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Description 1 online resource Series SpringerBriefs in quantitative finance, 2192-7006 SpringerBriefs in quantitative finance. Contents 880-01 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 880-01/(S 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 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 Analysis Mathematics Finance Numerical analysis Mathematical optimization Quantitative Finance Finance/Investment/Banking Calculus of Variations and Optimal Control; Optimization Bibliography Includes bibliographical references and index Notes English Subject Investment analysis -- Mathematical models Merton Model. Investments. Investments BUSINESS & ECONOMICS -- Investments & Securities -- General. Inversiones Investments Investment analysis -- Mathematical models Merton Model Portfolio Selection Stochastische optimale Kontrolle Hamilton-Jacobi-Differentialgleichung Ito-Formel Form Electronic book ISBN 9783642352027 3642352022 3642352014 9783642352010 1299197892 9781299197893

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