Risk-sensitive investment management / Mark H. A. Davis and Sébastien Lleo ; in-house editors, Lee Xin Ying, Philly Lim.

Format:

Book

Author/Creator:

Davis, M. H. A., author.

Lleo, Sébastien, author.

Contributor:

Lim, Philly, editor.

Ying, Lee Xin, editor.

Series:

Advanced series on statistical science & applied probability ; Volume 19.

Advanced Series on Statistical Science & Applied Probability ; Volume 19

Language:

English

Subjects (All):

Portfolio management--Mathematical models.

Portfolio management.

Investments--Mathematical models.

Investments.

Risk--Mathematical models.

Risk.

Physical Description:

1 online resource (414 p.)

Place of Publication:

Singapore : World Scientific Publishing, 2015.

Language Note:

English

Summary:

Over the last two decades, risk-sensitive control has evolved into an innovative and successful framework for solving dynamically a wide range of practical investment management problems. This book shows how to use risk-sensitive investment management to manage portfolios against an investment benchmark, with constraints, and with assets and liabilities. It also addresses model implementation issues in parameter estimation and numerical methods. Most importantly, it shows how to integrate jump-diffusion processes which are crucial to model market crashes. With its emphasis on the interconnecti

Contents:

Preface; Contents; Part I. Diffusion Models; 1. The Merton Problem; 1.1 Problem Formulation; 1.2 Logarithmic Utility; 1.3 Dynamic Programming; 1.4 Measure Change; 1.5 Duality Approach; 1.6 The Mutual Fund Theorem; 2. Risk-Sensitive Asset Management; 2.1 Financial Market and Investment Portfolio; 2.1.1 Financial Market; 2.1.2 Investment Portfolio; 2.2 Risk-Sensitive Asset Management Criterion; 2.3 Warm-Up: Solving the Risk-Sensitive Asset Management Problem When Asset and Factor Risks Are Uncorrelated; 2.4 Solving the Risk-Sensitive Asset Management Problem in the General Case

2.4.1 Measure Change2.4.2 Hamilton-Jacobi-Bellman PDE; 2.4.3 Deriving the Candidate Control; 2.4.4 Solving the HJB PDE; 2.4.5 Formalizing the Solution; 2.5 Making the Link with the Merton Problem; 2.6 Fund Separation Results; 2.6.1 The Kelly Portfolio; 2.6.2 General Case; 2.6.3 Fractional Kelly Strategies Revisited; 3. Managing Against a Benchmark; 3.1 Financial Market, Investment Portfolio and Benchmark; 3.1.1 Financial Market and Investment Portfolio; 3.1.2 Benchmark; 3.2 Risk-Sensitive Asset Management Criterion; 3.3 Solving the Benchmarked Asset Management Problem; 3.3.1 Measure Change

3.3.2 Hamilton-Jacobi-Bellman PDE3.3.3 Deriving the Candidate Control; 3.3.4 Solving the HJB PDE; 3.3.5 Formalizing the Solution; 3.4 Fund Separation Results; 3.5 Cases in Benchmarked Asset Management; 3.5.1 Uncorrelated Asset and Factor Risks; 3.5.2 Benchmark as a Static Portfolio of Risky Assets and the Bank Account; 4. Asset and Liability Management; 4.1 Assets, Liabilities and Equity; 4.1.1 The Funded Investor's Balance Sheet; 4.1.2 Financial Market and the Asset Portfolio; 4.1.3 Liabilities; 4.1.4 Equity and Leverage; 4.2 Risk-Sensitive Asset Management Criterion

4.3 Warm-Up: Uncorrelated Asset, Liability and Factor Noise4.4 Solving the Risk-Sensitive Asset and Liability Management Problem in the General Case; 4.4.1 Measure Change; 4.4.2 Hamilton-Jacobi-Bellman PDE; 4.4.3 Deriving the Candidate Control; 4.4.4 Solving the HJB PDE; 4.4.5 Formalizing the Solution; 4.5 Economic Interpretation and Fund Separation Theorems; 4.5.1 Understanding Optimal Leverage; 4.5.2 The Role of Risk Sensitivity in the Leverage; 4.5.3 The Role of Leverage in the Investment Strategy; 4.5.4 Fund Separation Theorem; 5. Investment Constraints; 5.1 Constrained Asset Management

5.1.1 Investment Constraints5.1.2 Asset Management Model; 5.1.3 Solving the Constrained Optimization Problem; 5.1.4 Fund Separation Results; 5.2 Constrained Benchmarked Asset Management; 5.3 Constrained Asset and Liability Management; 5.3.1 Investment Constraints; 5.3.2 Solving the Constrained Optimization Problem; 5.3.3 Fund Separation Results; 5.3.4 Application: Unconstrained Asset Allocation; 6. Infinite Horizon Problems; 6.1 Preliminary: A Few Useful Definitions and Properties from Dynamical Systems; 6.2 Asset Management Model; 6.2.1 The Riccati Equation; 6.2.2 Ergodic Bellman Equation

6.3 Benchmark

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

981-4578-05-3