Boolean-valued models as a foundation for locally $L^0$-convex analysis and Conditional set theory
Abstract
Locally -convex modules were introduced in [D. Filipovic, M. Kupper, N. Vogelpoth. Separation and duality in locally -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 -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.
Cite
@article{arxiv.1709.07185,
title = {Boolean-valued models as a foundation for locally $L^0$-convex analysis and Conditional set theory},
author = {Antonio Avilés and José Miguel Zapata},
journal= {arXiv preprint arXiv:1709.07185},
year = {2018}
}