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Vorbrink, Jörg: Valuation of financial contingent claims in the presence of model uncertainty. 2011
Inhalt
General introduction
Ambiguity/Knightian uncertainty
Ambiguity and financial markets
Scientific work on ambiguity in financial markets
Content of the thesis
American options with multiple priors in discrete time
Introduction
Financial markets and optimal stopping
The stochastic structure
The market model
The decision problem
The solution method
Options with monotone payoffs
Barrier options
Simple barrier options
Multiple barrier options
Multiple expiry options
Shout options
Quasi-convex payoffs
Conclusion
American options with multiple priors in continuous time
Introduction
The setting
The ambiguity model -ignorance
The financial market under -ignorance
American options under ambiguity aversion
A detour: reflected backward stochastic differential equations
Options with monotone payoffs
Exotic options
American up-and-in put option
Shout option
Conclusion
Financial markets with volatility uncertainty
Introduction
The market model
Arbitrage and contingent claims
The Markovian setting
Conclusion
Proofs and supplementary material
Proof of Theorem 2.3.1
Proof of Theorem 3.3.3
Proof of Theorem 3.4.1
Sublinear expectations
Sublinear expectation, G-Brownian motion and G-expectation
Stochastic calculus of Itô type with G-Brownian motion
Characterization of G-martingales