Template-Type:ReDIF-Paper 1.0  
Title:Approximation Pricing and the Variance-Optimal Martingale Measure
Author-Name:Schweizer, Martin
Classification-JEL:G13
Keywords:option pricing, variance-optimal martingale measure, backward stochastic differential equations,
	incomplete markets, adjustment process, mean-variance tradeoff, minimal signed martingale measure
Abstract: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.
Length: pages
Creation-Date: 1995-11
Revision-Date: 
Handle: RePEc:bon:bonsfb:336