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Discounting-invariant absence of arbitrage at the level of NUPBR
- Part of
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- Journal:
- Advances in Applied Probability , First View
- Published online by Cambridge University Press:
- 27 October 2026, pp. 1-30
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- Article
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We consider a financial market modelled by a general
$\mathbb{R}^d$-valued semimartingale S on 
$[0, \infty)$, without assuming the existence of a risk-free asset (savings account). We introduce a new absence-of-arbitrage concept, called 
${\underline{\textrm{NUPBR}}}$, which is a natural extension of the classic no unbounded profit with bounded risk (NUPBR) condition and which is in addition discounting-invariant for a large (but not maximal) class of discounters. We establish a dual characterisation of 
${\underline{\textrm{NUPBR}}}$ in terms of martingale properties for S, and we prove the existence of an ‘optimal’ self-financing value process which generalises the numeraire portfolio from the classic mathematical finance literature. We further introduce a notion of maximality for value processes and provide for that a dual characterisation which extends existing concepts to settings where value processes may fail to converge as 
$t\to\infty$.
