Time Consistent Bid-Ask Dynamic Pricing Mechanisms for Contingent Claims and Its Numerical Simulations Under Uncertainty
We study time consistent dynamic pricing mechanisms of European contingent claims under uncertainty by using G framework introduced by Peng (). We consider a financial market consisting of a riskless asset and a risky stock with price process modelled by a geometric generalized G-Brownian motion, which features the drift uncertainty and volatility uncertainty of the stock price process. Using the techniques on G-framework we show that the risk premium of the asset is uncertain and distributed with maximum distribution. A time consistent G-expectation is defined by the viscosity solution of the G-heat equation. Using the time consistent G-expectation we define the G dynamic pricing mechanism for the claim. We prove that G dynamic pricing mechanism is the bid-ask Markovian dynamic pricing mechanism. The full nonlinear PDE is derived to describe the bid (resp. ask) price process of the claim. Monotone implicit characteristic finite difference schemes for the nonlinear PDE are given, nonlinear iterative schemes are constructed, and the simulations of the bid (resp. ask) prices of contingent claims under uncertainty are implemented.
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.:
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1111.4298. 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: (arXiv administrators)
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.