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A note on the condition of no unbounded profit with bounded risk

Koichiro Takaoka () and Martin Schweizer

Finance and Stochastics, 2014, vol. 18, issue 2, 393-405

Abstract: As a corollary to Delbaen and Schachermayer’s fundamental theorem of asset pricing (Delbaen in Math. Ann. 300:463–520, 1994 ; Stoch. Stoch. Rep. 53:213–226, 1995 ; Math. Ann. 312:215–250, 1998 ), we prove, in a general finite-dimensional semimartingale setting, that the no unbounded profit with bounded risk (NUPBR) condition is equivalent to the existence of a strict sigma-martingale density. This generalizes the continuous-path result of Choulli and Stricker (Séminaire de Probabilités XXX, pp. 12–23, 1996 ) to the càdlàg case and extends the recent one-dimensional result of Kardaras (Finance and Stochastics 16:651–667, 2012 ) to the multidimensional case. It also refines partially the second main result of Karatzas and Kardaras (Finance Stoch. 11:447–493, 2007 ) concerning the existence of an equivalent supermartingale deflator. The proof uses the technique of numéraire change. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: NUPBR; Strict sigma-martingale density; Equivalent local martingale deflator; Fundamental theorem of asset pricing; 91B70; 60G48; C60; G13 (search for similar items in EconPapers)
Date: 2014
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