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Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension

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  • Winslow Strong

Abstract

The purpose of this paper is two-fold. First is to extend the notions of an n-dimensional semimartingale and its stochastic integral to a piecewise semimartingale of stochastic dimension. The properties of the former carry over largely intact to the latter, avoiding some of the pitfalls of infinite-dimensional stochastic integration. Second is to extend two fundamental theorems of asset pricing (FTAPs): the equivalence of no free lunch with vanishing risk to the existence of an equivalent sigma-martingale measure for the price process, and the equivalence of no arbitrage of the first kind to the existence of an equivalent local martingale deflator for the set of nonnegative wealth processes.

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  • Winslow Strong, 2011. "Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension," Papers 1112.5340, arXiv.org.
  • Handle: RePEc:arx:papers:1112.5340
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    References listed on IDEAS

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    1. Y.M. Kabanov & D.O. Kramkov, 1998. "Asymptotic arbitrage in large financial markets," Finance and Stochastics, Springer, vol. 2(2), pages 143-172.
    2. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
    3. Winslow Strong & Jean-Pierre Fouque, 2011. "Diversity and arbitrage in a regulatory breakup model," Annals of Finance, Springer, vol. 7(3), pages 349-374, August.
    4. Balbás, Alejandro & Downarowicz, Anna, 2004. "Infinitely many securities and the fundamental theorem of asset pricing," DEE - Working Papers. Business Economics. WB wb043513, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    5. De Donno, M. & Guasoni, P. & Pratelli, M., 2005. "Super-replication and utility maximization in large financial markets," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 2006-2022, December.
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