## Paris-Princeton Lectures on Mathematical Finance 2010Areski Cousin, Stéphane Crépey, Olivier Guéant, David Hobson, Monique Jeanblanc, Jean-Michel Lasry, Jean-Paul Laurent, Pierre-Louis Lions, Peter Tankov The Paris-Princeton Lectures in Financial Mathematics, of which this is the fourth volume, publish cutting-edge research in self-contained, expository articles from outstanding specialists - established or on the rise! The aim is to produce a series of articles that can serve as an introductory reference source for research in the field. The articles are the result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with five articles by: 1. Areski Cousin, Monique Jeanblanc and Jean-Paul Laurent, 2. Stéphane Crépey, 3. Olivier Guéant, Jean-Michel Lasry and Pierre-Louis Lions, 4. David Hobson and 5. Peter Tankov. |

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### Contents

Hedging CDO Tranches in a Markovian Environment | 1 |

About the Pricing Equations in Finance | 63 |

Mean Field Games and Applications | 204 |

The Skorokhod Embedding Problemand ModelIndependent Bounds for Option Prices | 267 |

Pricing and Hedging in Exponential Levy Models Reviewof Recent Results | 319 |

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agents application arbitrage asset assume assumption Bielecki Black–Scholes bound Brownian motion calibration call protection CDO tranche computed consider contagion continuous credit default swap credit deltas credit derivatives credit spreads default swap index defined Definition delta hedging denote deterministic distribution dynamics equity tranche exponential Lévy models financial derivative finite function Gaussian copula given hedging strategies implied volatility inequality initial condition jump jump-diffusion Lemma Lévy process local martingale loss intensities Markov chain Markovian martingale mathematical maturity mean field games minimal N-player game Note number of defaults optimal option prices payoff PDEs portfolio premium price process pricing and hedging proof Proposition R2BSDE random variable reflected BSDEs resp RIBSDE risk-neutral satisfies Sect Skorokhod embedding problem stochastic differential equation stopping Theorem unique viscosity solutions