22 documents found

Article / Chapter

Quadratic hedging in affine stochastic volatility models

Dordrecht: Springer Science + Business Media, 2009
Article / Chapter

sigma-Localization and sigma-Martingales

Philadelphia, PA: Society for Industrial and Applied Mathematics, 2004
Article / Chapter

The cumulant process and Esscher's change of measure

Berlin; Heidelberg: Springer, 2002

On Using Shadow Prices for the Asymptotic Analysis of Portfolio Optimization...

This thesis contains three scientific articles on the problem of utility maximization in a financial market with proportional transaction costs. One of the most revealing approaches to this problem consists in passing to the asymptotic analysis of the impact of small transaction costs, where the maximum...

The Heath-Jarrow-Morton approach for modelling stock options

This thesis aims at transferring the philosophy behind Heath-Jarrow-Mor-ton to the modelling of call options. Moreover, arbitrage-free models as well as the necessary techniques are developed in this thesis.

Second-order approximations to pricing and hedging in presence of jumps...

This thesis deals with two basic problems of Mathematical Finance, namely the pricing and hedging of European-style derivatives. We analyze these questions in models that describe the asset underlying the derivative by a process with jumps and stochastic volatility. However, we are not interested in...

Hedging in affine stochastic volatility models

Typically an investor incurs risk by issuing a contingent claim. She can try to reduce this risk by trading in the underlying asset according to a strategy which is in some sense appropriate. In an incomplete financial market there usually are several meaningful choices for the determination of such...

Representable Options

We call a given American option representable if there exists a European claim which dominates the American payoff function at any time and such that the values of the two options coincide within the continuation set associated to the American option. This mathematical concept has interesting implications...

Approximate pricing of barrier options in Lévy models

This thesis deals with pricing of a certain type of derivatives, namely European barrier options. We consider the question of pricing this option in geometric Lévy models, which in contrast to the famous Black-Scholes model allow jumps in the stock price. This increases the difficulty of computing an...

Portfolio optimization in arbitrary dimensions in the presence of small...

This thesis deals with the problem of maximizing the expected utility of terminal wealth in financial markets with an arbitrary number of risky assets in the presence of small bid-ask spreads. The goal is to determine an asymptotically optimal trading strategy and to quantify the asymptotic welfare impact...