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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Davis, M.H.A. Risk-sensitive investment management (OCoLC)889705605 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
M H A Davis; Sébastien Lleo |

ISBN: | 9789814578059 9814578053 |

OCLC Number: | 890321032 |

Description: | 1 online resource (xvi, 397 pages). |

Contents: | pt. 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. 2.2. 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. 2.5. Making the link with the Merton problem. 2.6. Fund separation results -- 3. Managing against a benchmark. 3.1. Financial market, investment portfolio and benchmark. 3.2. Risk-sensitive asset management criterion. 3.3. Solving the benchmarked asset management problem. 3.4. Fund separation results. 3.5. Cases in benchmarked asset management -- 4. Asset and liability management. 4.1. Assets, liabilities and equity. 4.2. Risk-sensitive asset management criterion. 4.3. Warm-up: Uncorrelated asset, liability and factor noise. 4.4. Solving the risk-sensitive asset and liability management problem in the general case -- 5. Investment constraints. 5.1. Constrained asset management. 5.2. Constrained benchmarked asset management. 5.3. Constrained asset and liability management -- 6. Infinite horizon problems. 6.1. Preliminary: A few useful definitions and properties from dynamical systems. 6.2. Asset management model. 6.3. Benchmark. 6.4. ALM -- pt. II. Jump-diffusion models. 7. Jumps in asset prices. 7.1. Poisson point processes and jump-diffusion SDEs. 7.2. Analytical setting for asset allocation. 7.3. Problem setup. 7.4. Main result. 7.5. Maximisation of the Hamiltonian. 7.6. Verification theorems. 7.7. Existence of a classical solution. 7.8. Admissibility of the optimal control policy -- 8. General jump-diffusion setting. 8.1. Analytical setting. 8.2. Dynamic programming and the value function. 8.3. Existence of a classical (C[symbol]) solution. 8.4. Identifying the optimal strategy -- 9. Fund separation and fractional Kelly strategies. 9.1. Setting. 9.2. No jumps in asset prices: [symbols]. 9.3. The Kelly portfolio. 9.4. The intertemporal hedging portfolio. 9.5. Uncorrelated asset and factor diffusion: [symbol] = 0. 9.6. General fund separation theorem and fractional Kelly strategies -- 10. Managing against a benchmark: Jump-diffusion case. 10.1. Introduction. 10.2. Financial market, investment portfolio and benchmark. 10.3. Dynamic programming and the value function. 10.4. Existence of a classical (C[symbol]) solution under affine drift assumptions. 10.5. Existence of a classical (C[symbol]) solution under standard control assumptions. 10.6. Fund separation theorem -- 11. Asset and liability management: Jump-diffusion case. 11.1. Introduction. 11.2. Financial market, investment portfolio and liability. 11.3. Formulation of the asset and liability management problem. 11.4. Dynamic programming and the value function. 11.5. Solving the ALM problem under affine drift assumptions. 11.6. Solving the ALM problem under standard control assumptions. 11.7. Admissibility of the optimal control policy. 11.8. Fund separation theorem -- pt. III. Implementation. 12. Factor and securities models. 12.1. Interest rates and bond prices. 12.2. Addressing the potential negativity of factors -- 13. Case studies. 13.1. Asset management: Does the factor X matter? 13.2. Benchmarks: From active management to benchmark (super) replication. 13.3. Asset and liability management: Nature of the liability. 13.4. Asset and liability management: The danger of overbetting -- 14. Numerical methods. 14.1. Preliminary: The stochastic control problem under the measure P. 14.2. Approximation in policy space. 14.3. Kushner's method -- 15. Factor estimation: Filtering and Black-Litterman. 15.1. Estimation and filtering. 15.2. Latent variable factors. 15.3. Black-Litterman in continuous time. 15.4. Concluding remarks. |

Series Title: | Advanced series on statistical science & applied probability, v. 19. |

Responsibility: | Mark H.A. Davis, Sébastien Lleo. |

### Abstract:

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 interconnection between mathematical techniques and real-world problems, this book will be of interest to both academic researchers and money managers. Risk-sensitive investment management links stochastic control and portfolio management. Because of its distinct emphasis on integrating advanced theoretical concepts into practical dynamic investment management tools, this book stands out from the existing literature in fundamental ways. It goes beyond mainstream research in portfolio management in a traditional static setting. The theoretical developments build on contemporary research in stochastic control theory, but are informed throughout by the need to construct an effective and practical framework for dynamic portfolio management. This book fills a gap in the literature by connecting mathematical techniques with the real world of investment management. Readers seeking to solve key problems such as benchmarked asset management or asset and liability management will certainly find it useful.

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