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Diffusion-based models for financial markets without martingale measures

Claudio Fontana 1 Wolfgang Runggaldier 2 
1 MATHRISK - Mathematical Risk handling
Inria Paris-Rocquencourt, UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech
Abstract : In this paper we consider a general class of diffusion-based models and show that, even in the absence of an Equivalent Local Martingale Measure, the financial market may still be viable, in the sense that strong forms of arbitrage are excluded and portfolio optimisation problems can be meaningfully solved. Relying partly on the recent literature, we provide necessary and sufficient conditions for market viability in terms of the market price of risk process and martingale deflators. Regardless of the existence of a martingale measure, we show that the financial market may still be complete and contingent claims can be valued under the original (real-world) probability measure, provided we use as numeraire the Growth-Optimal Portfolio.
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Submitted on : Saturday, August 24, 2013 - 3:42:06 PM
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Claudio Fontana, Wolfgang Runggaldier. Diffusion-based models for financial markets without martingale measures. Francesca Biagini and Andreas Richter and Harris Schlesinger. Risk Measures and Attitudes, Springer, pp.45-81, 2013, EAA Series, 1869-6929. ⟨10.1007/978-1-4471-4926.2_4⟩. ⟨hal-00853874⟩



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