## Optimization Methods in FinanceOptimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses. |

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### Contents

1 | |

theory and algorithms | 15 |

assetliability cashﬂow matching | 41 |

asset pricing and arbitrage | 62 |

theory and algorithms | 80 |

volatility estimation | 112 |

theory and algorithms | 121 |

portfolio optimization | 138 |

constructing an index fund | 212 |

Dynamic programming methods | 225 |

option pricing | 240 |

structuring assetbacked securities | 248 |

theory and algorithms | 255 |

ValueatRisk | 271 |

assetliability management | 279 |

theory and tools | 292 |

Conic optimization tools | 168 |

Conic optimization models in ﬁnance | 178 |

theory and algorithms | 192 |

Robust optimization models in ﬁnance | 306 |

338 | |

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### Common terms and phrases

algorithm approach arbitrage arbitrage opportunities assume basic variables bond bound branch call option cash ﬂow central path coefﬁcient compute conic optimization consider constraints convex convex function corresponding costs covariance matrix decision variables deﬁned deﬁnition denote dual dynamic programming equation estimate example Exercise expected return f(xk feasible set feasible solution ﬁnance ﬁnancial ﬁnd ﬁnite ﬁrst ﬁxed formulation given index fund inequality integer linear program integer program interest rate investment investor iteration linear program maximize MILP minimize minx Newton’s method node nonlinear programming nonnegative objective function objective value obtain optimal solution optimization problem option prices payoff positive semideﬁnite proﬁt random variable recourse risk robust optimization satisﬁes second-order cone Section simplex method solve SOLVER spline stage stochastic program strategy strike price tableau theorem uncertain parameters uncertainty set vector volatility

### Popular passages

Page 338 - In H. Frenk, K. Roos, T. Terlaky, and S. Zhang, editors, High performance optimization, pages 197-232.

Page 338 - Computational Study of a Family of Mixed-Integer Quadratic Programming Problems,” Mathematical Programming 74, 121-140 (1996).

Page 339 - Kasai model: an asset/liability model for a Japanese insurance company using multistage stochastic programming. Interfaces 24 (1994) 29-49.