Anticipative stochastic calculus with applications to financial markets
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Date
2010-03-17T10:19:33Z
Authors
Pamen, Olivier Menoukeu
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Abstract
In this thesis, we study both local time and Malliavin calculus and their application
to stochastic calculus and nance. In the rst part, we analyze three aspects of applications
of local time. We rst focus on the existence of the generalized covariation
process and give an approximation when it exists. Thereafter, we study the decomposition
of ranked semimartingales. Lastly, we investigate an application of ranked
semimartingales to nance and particularly pricing using Bid-Ask. The second part
considers three problems of optimal control under asymmetry of information and
also the uniqueness of decomposition of \Skorohod-semimartingales". First we look
at the problem of optimal control under partial information, and then we investigate
the uniqueness of decomposition of \Skorohod-semimartingales" in order to study
both problems of optimal control and stochastic di erential games for an insider.