Characterisation of L⁰-boundedness for a general set of processes with no strictly positive element
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Date
2022-05
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Journal Article
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Abstract
We consider a general set X of adapted nonnegative stochastic processes in infinite continuous time. X is assumed to satisfy mild convexity conditions, but in contrast to earlier papers need not contain a strictly positive process. We introduce two boundedness conditions on X — DSV corresponds to an asymptotic L0-boundedness at the first time all processes in X vanish, whereas NUPBRloc states that Xt = {Xt : X ∈ X } is bounded in L0 for each t ∈ [0, ∞). We show that both conditions are equivalent to the existence of a strictly positive adapted process Y such that XY is a supermartingale for all X ∈ X , with an additional asymptotic strict positivity property for Y in the case of DSV.
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published
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Volume
147
Pages / Article No.
51 - 75
Publisher
Elsevier
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Subject
L⁰-boundedness; Supermartingale; NUPBR; Viability; Set of wealth processes; Absence of numeraire; Fundamental theorem of asset pricing
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03658 - Schweizer, Martin / Schweizer, Martin
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Is new version of: http://hdl.handle.net/20.500.11850/464039