Boolean-valued models as a foundation for locally L⁰-convex analysis and Conditional set theory

2017/09/21 by Avilés, Antonio, Zapata, José Miguel · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1709.07185

Abstract

Locally L⁰-convex modules were introduced in [D. Filipovic, M. Kupper, N. Vogelpoth. Separation and duality in locally L⁰-convex modules. J. Funct. Anal. 256(12), 3996-4029 (2009)] as the analytic basis for the study of multi-period mathematical finance. Later, the algebra of conditional sets was introduced in [S. Drapeau, A. Jamneshan, M. Karliczek, M. Kupper. The algebra of conditional sets and the concepts of conditional topology and compactness. J. Math. Anal. Appl. 437(1), 561-589 (2016)]. By means of Boolean-valued models and its transfer principle we show that any known result on locally convex spaces has a transcription in the frame of locally L⁰-convex modules which is also true, and that the formulation in conditional set theory of any theorem of classical set theory is also a theorem. We propose Boolean-valued analysis as an analytic framework for the study of multi-period problems in mathematical finance.

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