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Order book models, signatures and numerical approximations of rough differential equations

Abstract:

We construct a mathematical model of an order driven market where traders can submit limit orders and market orders to buy and sell securities. We adapt the notion of no free lunch of Harrison and Kreps and Jouini and Kallal to our setting and we prove a no-arbitrage theorem for the model of the order driven market. Furthermore, we compute signatures of order books of different financial markets. Signatures, i.e. the full sequence of definite iterated integrals of a path, are one of the fu...

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Institution:
University of Oxford
Research group:
Stochastic Analysis Group, Oxford-Man Institute of Quantitative Finance
Oxford college:
Magdalen College
Department:
Mathematical,Physical & Life Sciences Division - Mathematical Institute

Contributors

Role:
Supervisor
Publication date:
2012
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
Oxford University, UK
URN:
uuid:264e96b3-f449-401b-8768-337acab59cab
Local pid:
ora:6069

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