Coherent price systems and uncertainty-neutral valuation

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Working Papers ; No. 464

Classification and Topics

• Classification: Wirtschaft ; Contingent Pricing; Futures Pricing; option pricing ; Information and Market Efficiency; Event Studies; Insider Trading ; Value Theory ; Incomplete Markets ; Existence and Stability Conditions of Equilibrium
• Subject: 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

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Beißner, Patrick
• Event: Veröffentlichung
• (who): Bielefeld University, Institute of Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2012

Further information

• Handle: http://hdl.handle.net/10419/81124
• Last update: 10.03.2025, 11:45 AM CET