Appleby, J. A. D. and Riedle, M. and Swords, C. (2010) Bubbles and crashes in a Black-Scholes model with delay. [MIMS Preprint]
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Abstract
This paper studies the asymptotic behaviour of an affine stochastic functional differential equation modelling the evolution of the cumulative return of a risky security. In the model, the traders of the security determine their investment strategy by comparing short-- and long--run moving averages of the security's returns. We show that the cumulative returns either obey the Law of the Iterated Logarithm, but have dependent increments, or exhibit asymptotic behaviour that can be interpreted as a runaway bubble or crash.
| Item Type: | MIMS Preprint |
|---|---|
| Uncontrolled Keywords: | stochastic functional differential equation, resolvent, renewal equation, Brownian motion, Law of the Iterated Logarithm, Efficient Market Hypothesis |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 91 Game theory, economics, social and behavioral sciences |
| Depositing User: | Dr Markus Riedle |
| Date Deposited: | 24 May 2010 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1455 |
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