## Numerical Methods in FinanceNumerical methods in finance has recently emerged as a new discipline at the intersection of probability theory, finance and numerical analysis. This book describes a wide variety of numerical methods used in financial analysis: computation of option prices, especially American option prices, by finite difference and other methods; numerical solution of portfolio management strategies; statistical procedures, identification of models; Monte Carlo methods; and numerical implications of stochastic volatilities. Lucid and concise, it covers both mathematical matters and practical issues in numerical problems. This book is an ideal resource for economists, probabilists and applied mathematicians working in finance. |

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### Contents

Nigel J Newton ContinuousTime Monte Carlo Methods and Variance | 22 |

Broadie J Detemple Recent Advances in Numerical Methods | 43 |

A Comparison of Numerical | 67 |

Adriaan Joubert L C G Rogers Fast Accurate and Inelegant Valuation | 88 |

Nathalie Pistre Groupe CERAM Rue Dostoievski BP 085 06902 Sophia | 109 |

E Fournie J M Lasry P L Lions Some Nonlinear Methods for Studying | 115 |

E Fournie J M Lasry N Touzi Monte Carlo Methods for Stochastic | 146 |

Agnes Sulem Dynamic Optimization for a Mixed Portfolio with | 165 |

N El Karoui M C Quenez Imperfect Markets and Backward Stochastic | 181 |

N El Karoui E Pardoux M C Quenez Reflected Backward SDEs | 215 |

Chevance Numerical Methods for Backward Stochastic Differential | 232 |

Agnes Tourin Thaleia Zariphopoulou Viscosity Solutions and Numerical | 245 |

Renzo G Avesani Pierre Bertrand Does Volatility Jump or Just Diffuse? | 270 |

Peter Bossaerts Bas Werker MartingaleBased Hedge Error Control | 290 |

Claude Henin Nathalie Pistre The Use of SecondOrder Stochastic | 305 |

### Common terms and phrases

algorithm American option American Put American Put Options Applications approximation assumptions asymptotic binomial method Black-Scholes model bounded Broadie Brownian motion BSDE call option classical coefficients compute concave constant contingent claim continuous control problem convergence defined denote derivatives Detemple deterministic diffusion process discrete dynamic programming estimator example exercise boundary formula given hedge portfolio hedging strategy implied volatility incomplete market interest rate Journal of Financial Karatzas Karoui large deviations linear Lions Markov martingale Math matrix Monte Carlo methods nonlinear numerical methods numerical schemes optimal stopping option pricing parameters Pardoux payoff Peng probability proof Proposition Quenez random RBSDE recursive utility risk risky asset satisfies Scholes Section simulation solve square integrable standard stochastic differential equations stochastic volatility stochastic volatility model stock price theory tion Touzi tracking error transaction costs unique solution Valuation value function variational inequality viscosity solutions Wiener process