Contrôle stochastique appliqué à la ﬁnance
AbstractThis PhD thesis considers the optimal trading problem from the stochastic control approach and consists of four parts. In the first part, we begin with the study of the impacts generated by volumes on the price process. We introduce a structural model in which price movements are due to not only the last trade’s volume but also to those of earlier trades, weakened by a decay factor. Considering a similar continuous version, we provide a condition ensuring the optimality of a strategy for the minimization of the execution cost in a mean-variance framework, and solve it numerically. In the second part, we propose a general model to optimize the way trading algorithms are used. Using an impulse control approach, we model the execution of a large order by a sequence (τi,δi,Ei)i, which is defined so that the i-th slice is executed in [τi,τi+δi] with parameter Ei. We characterize the value function as a viscosity solution of a system of PDE. We provide a numerical scheme and prove its convergence. Numerical illustrations are given for a real case. We deal with the problem of pricing an option on the book liquidation in presence of impact where the classical pricing by neutral risk measure fails. We begin with an abstract model generalized from the work of Bouchard- Eile-Touzi (2008), and then apply to compute the price of a VWAP guaranteed contract. We establish in the last part an equivalence result between stochastic target problems and standard optimal control. We derive the classical HJB equation from the PDE obtained in the stochastic target framework.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoThis book is provided by Paris Dauphine University in its series Economics Thesis from University Paris Dauphine with number 123456789/7237 and published in 2011.
Ordres de bourse; Processus stochastiques;
Find related papers by JEL classification:
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Alexandre Faure).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.