Approximation Pricing and the Variance-Optimal Martingale Measure
Let X be a seminmartingale and Teta the space of all predictable X-integrable processes teta such that integral tetat dX is inthe space S square of semimartingales. We consider the problem of approximating a given random variable H element of L square (P) by the sum of a constant c and a stochastic integral of 0 to t with teta s and dXs, with respect to the L square (P)-norm. This problem comes from financial mathematics where the optimal constant V zero can be interpreted as an approximation price for the contingent claim H. An elementary computation yields V zero as the expectation of H under the variance-optimal signed Teta-martingale measure P~, and this leads us to study &Ptilde in more detail. In the case of finite discrete time, we explicitly construct P~ by backward recursion, and we show that P~ is typically not a probability, but only a signed measure. In a continuous-time framework, the situation becomes rather different: We prove that P~ is nonnegative if X has continuous paths and satisfies a very mild no-arbitrage condition. As an application, we show how to obtain the optimal integrand xi element teta in feedback form with the help of a backward stochastic differential equation.
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
|Date of creation:||Nov 1995|
|Contact details of provider:|| Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany|
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de
When requesting a correction, please mention this item's handle: RePEc:bon:bonsfb:336. 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: (BGSE Office)
If references are entirely missing, you can add them using this form.