Titlebook: Advanced Mathematical Methods for Finance; Giulia Di Nunno,Bernt Øksendal Book 2011 Springer-Verlag Berlin Heidelberg 2011 Calculus of va

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https://doi.org/10.1007/978-3-663-09423-4l. Our main assumption is the commuting property of the drift and diffusion vector fields with respect to the usual Lie bracket. This result is next applied for a system of Burgers equations with stochastic perturbations and also to the computations of some expectations of functionals depending on t

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Biographietheoretische Forschungshaltung, jumps. In this paper we consider a dense subclass of such models and develop analytically tractable formulae for the prices of a range of first-generation exotic derivatives. We provide closed-form formulae for the Fourier transforms of vanilla and forward starting option prices as well as a formul

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Giulia Di Nunno,Bernt ØksendalPresents new models, new methods and new results in quantitative finance.Includes an analysis of new financial products such as exotic derivatives and liquidity models.Shows an application-oriented pr

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https://doi.org/10.1007/978-3-663-09422-7We survey several models of liquidity and liquidity-related problems such as optimal execution of a large order, hedging and super-hedging options for a large trader, utility maximization in illiquid markets, and price impact models with price manipulation strategies.

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Jürgen Baumert,Kai Maaz,Ulrich Trautweintation results of conditional convex risk measures, and we characterize various time consistency properties of dynamic risk measures in terms of acceptance sets, penalty functions, and by supermartingale properties of risk processes and penalty functions.

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Dirk Randoll,Ines Graudenz,Jürgen Petersults on arbitrage opportunities, hedging, and option pricing in these models. We summarize some recent results on fractional Black & Scholes pricing model with transaction costs. We end the paper by giving some approximation results and indicating some open problems related to the paper.

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Fallkontrastierung und Typenbildung,a degenerate parabolic semilinear equation, and we state existence, uniqueness, and regularity results in the framework of viscosity solutions. These results allow a complete justification of the model. We also obtain a convergence result of a numerical scheme to the solution of the valuation equation.