Coherent price systems and uncertainty-neutral valuation - Patrick Beißner (Bielefeld University, Institute of Mathematical Economics (IMW), 2012)
We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of arbitrage and the existence of an equivalent martingale measure is a folk theorem, see Harrison and Kreps (1979). We establish a microeconomic foundation of sublinear price systems and present an extension result. In this context we introduce a prior dependent notion of marketed spaces and viable price systems. We associate this extension with a canonically altered concept of equivalent symmetric martingale measure sets, in a dynamic trading framework under absence of prior depending arbitrage. We prove the existence of such sets when volatility uncertainty is modeled by a stochastic di erential equation, driven by Peng's G-Brownian motions.
Keywords: G13; G14; D46; D52; C62; 330; mutually singular priors; uncertain volatility; sublinear expectation; viability of sublinear price systems; arbitrage; equivalent symmetric martingale measures set (EsMM set); symmetric martingales; Girsanov for G-Brownian motion; Arbitrage Pricing; Volatilität; Risiko; Erwartungstheorie; Martingale; Theorie