Characterisation of L⁰-boundedness for a general set of processes with no strictly positive element


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Date

2022-05

Publication Type

Journal Article

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yes

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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.

Publication status

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

Organisational unit

03658 - Schweizer, Martin / Schweizer, Martin check_circle

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