## Advanced Financial ModellingHansjörg Albrecher, Wolfgang J. Runggaldier, Walter Schachermayer This book is a collection of state–of–the–art surveys on various topics in mathematical finance, with an emphasis on recent modelling and computational approaches. The volume is related to a 'Special Semester on Stochastics with Emphasis on Finance' that took place from September to December 2008 at the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences in Linz, Austria. |

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### Contents

1 | |

27 | |

Viscosity solutions to optimal portfolio allocation problems in models with random time changes and transaction costs | 53 |

Discretetime approximation of BSDEs and probabilistic schemes for fully nonlinear PDEs | 91 |

theory and applications | 125 |

Multilevel quasiMonte Carlo path simulation | 165 |

an application to asset backed securities | 183 |

Adaptive variance reduction techniques in finance | 205 |

Optimal consumption and investment with bounded downside risk measures for logarithmic utility functions | 245 |

A review of some recent results on Malliavin Calculus and its applications | 275 |

existence related concepts and applications | 303 |

A worstcase approach to continuoustime portfolio optimisation | 327 |

Time consistency and information monotonicity of multiperiod acceptability functionals | 347 |

Optimal investment and hedging under partial and inside information | 371 |

Investmentconsumption choice in illiquid markets with random trading times | 411 |

Optimal asset allocation in a stochastic factor model an overview and open problems | 427 |

Regularisation of inverse problems and its application to the calibration of option price models | 223 |

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Advanced Financial Modelling Hansjörg Albrecher,Wolfgang J. Runggaldier,Walter Schachermayer Limited preview - 2009 |

### Common terms and phrases

admissible algorithm applications approximation asset price assume assumptions Black–Scholes Brownian motion BSDEs calibration compute condition consider constant convergence rate convex crash deﬁned deﬁnition denote density derivative deterministic discretisation distribution dynamic estimator exists exponential filtration ﬁrst formula G Rd given Hence Heston model ill-posed ill-posed problems implies inequality integral inverse problem jumps L´evy Lemma linear Lipschitz Lipschitz continuous local volatility Malliavin Malliavin Calculus mapping martingale measure Mathematical Finance method Monte Carlo Moreover multi-period nonlinear Normal one-factor numeraire portfolio numerical obtain optimal portfolio optimisation problem option price parameter portfolio process Proof Proposition Qngd random variable Riccati equations risk measure satisﬁes satisfying Section semimartingales short rate model simulation space stochastic differential equations stochastic volatility stock price Theorem unique utility function value function variance vector viscosity solution wealth process worst-case