A contribution in stochastic control applied to finance and insurance
- Bouchard, Bruno
The aim of this thesis is to investigate some solutions to the pricing of contingent claims in incomplete markets. We first consider the stochastic targetintroduced by Soner and Touzi (2002) for the general super-replication problem, and extended by Bouchard, Elie and Touzi (2009) in order to deal with more general approaches. We first generalize the work of Bouchard et al to a framework where the discusions are subject to jumps. In our particular settings, we need to consider a control taking the form of unbounded maps, which has non-trivial impacts on the derivation of the associated PDE. Our second contribution consists in establishing a version of stochastic target problems which is robust to model uncertainty. We provide, in a general setup, a relaxed geometric dynamic programming principle for this problem and derive, for the case of a controlled SDE, the corresponding dynamic programming equation in the sense of viscosity solutions. We consider an example of partial hedging under Knightian uncertainty. Finally, we focus on the problem of pricing hybrid claims. More specifically, we intend to give a sufficient condition for a (very popular) pricing rule, combining actuarial diversification with arbitrage free replication arguments, to hold.
|This book is provided by Paris Dauphine University in its series Economics Thesis from University Paris Dauphine with number 123456789/10711 and published in 2012.|
|Contact details of provider:|| Web page: http://www.dauphine.fr/en/welcome.html|
More information through EDIRC
Find related papers by JEL classification:
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Schweizer, Martin, 1999. "A guided tour through quadratic hedging approaches," SFB 373 Discussion Papers 1999,96, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
When requesting a correction, please mention this item's handle: RePEc:dau:thesis:123456789/10711. See general 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 references are entirely missing, you can add them using this form.
Follow series, journals, authors & more
New papers by email
Subscribe to new additions to RePEc
Public profiles for Economics researchers
Various rankings of research in Economics & related fields
Who was a student of whom, using RePEc
Curated articles & papers various economics topics
Upload your paper to be listed on RePEc and IDEAS
Blog aggregator for economics research
Cases of plagiarism in Economics
Job Market Papers
RePEc working paper series dedicated to the job market
Pretend you are at the helm of an economics department
Services from the StL Fed
Data, research, apps & more from the St. Louis Fed