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dc.contributor.advisor Mhlanga, F. J.
dc.contributor.advisor Łochowski, R. M. Galane, Lesiba Charles 2021-06-25T08:50:48Z 2021-06-25T08:50:48Z 2021
dc.description Thesis (Ph.D. (Applied Mathematics)) -- University of Limpopo, 2021 en_US
dc.description.abstract Vovk and Shafer, [41], introduced game-theoretic framework for probability in mathematical finance. This is a new trend in financial mathematics in which no probabilistic assumptions on the space of price paths are made. The only assumption considered is the no-arbitrage opportunity widely accepted by the financial mathematics community. This approach rests on game theory rather than measure theory. We deal with various properties and constructions of quadratic variation for model-free càdlàg price paths and integrals driven by such paths. Quadratic variation plays an important role in the analysis of price paths of financial securities which are modelled by Brownian motion and it is sometimes used as the measure of volatility (i.e. risk). This work considers mainly càdlàg price paths rather than just continuous paths. It turns out that this is a natural settings for processes with jumps. We prove the existence of partition independent quadratic variation. In addition, following assumptions as in Revuz and Yor’s book, the existence and uniqueness of the solutions of SDEs with Lipschitz coefficients, driven by model-free price paths is proven. en_US
dc.description.sponsorship National Research Foundation (NRF) en_US
dc.format.extent vii, 88 leaves en_US
dc.language.iso en en_US
dc.relation.requires PDF en_US
dc.subject Mathematical finance en_US
dc.subject Mathematical models en_US
dc.subject Calculus en_US
dc.subject Price paths en_US
dc.subject.lcsh Finance -- Mathematical models en_US
dc.subject.lcsh Mathematical models en_US
dc.subject.lcsh Calculus en_US
dc.title Properties and calculus on price paths in the model-free approach to the mathematical finance en_US
dc.type Thesis en_US

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