Matches in SemOpenAlex for { <https://semopenalex.org/work/W4287760621> ?p ?o ?g. }
Showing items 1 to 51 of
51
with 100 items per page.
- W4287760621 abstract "We give a definitive treatment of duality for optimal consumption over the infinite horizon, in a semimartingale incomplete market satisfying no unbounded profit with bounded risk (NUPBR). Rather than base the dual domain on (local) martingale deflators, we use a class of supermartingale deflators such that deflated wealth plus cumulative deflated consumption is a supermartingale for all admissible consumption plans. This yields a strong duality, because the enlarged dual domain of processes dominated by deflators is naturally closed, without invoking its closure. In this way we automatically reach the bipolar of the set of deflators. We complete this picture by proving that the set of processes dominated by local martingale deflators is dense in our dual domain, confirming that we have identified the natural dual space. In addition to the optimal consumption and deflator, we characterise the optimal wealth process. At the optimum, deflated wealth is a supermartingale and a potential, while deflated wealth plus cumulative deflated consumption is a uniformly integrable martingale. This is the natural generalisation of the corresponding feature in the terminal wealth problem, where deflated wealth at the optimum is a uniformly integrable martingale. We use no constructions involving equivalent local martingale measures. This is natural, given that such measures typically do not exist over the infinite horizon and that we are working under NUPBR, which does not require their existence. The structure of the duality proof reveals an interesting feature compared with the terminal wealth problem. There, the dual domain is $L^{1}$-bounded, but here the primal domain has this property, and hence many steps in the duality proof show a marked reversal of roles for the primal and dual domains, compared with the proofs of Kramkov and Schachermayer." @default.
- W4287760621 created "2022-07-26" @default.
- W4287760621 creator A5049267532 @default.
- W4287760621 date "2020-06-08" @default.
- W4287760621 modified "2023-09-23" @default.
- W4287760621 title "Duality for optimal consumption under no unbounded profit with bounded risk" @default.
- W4287760621 doi "https://doi.org/10.48550/arxiv.2006.04687" @default.
- W4287760621 hasPublicationYear "2020" @default.
- W4287760621 type Work @default.
- W4287760621 citedByCount "0" @default.
- W4287760621 crossrefType "posted-content" @default.
- W4287760621 hasAuthorship W4287760621A5049267532 @default.
- W4287760621 hasBestOaLocation W42877606211 @default.
- W4287760621 hasConcept C134306372 @default.
- W4287760621 hasConcept C144237770 @default.
- W4287760621 hasConcept C202444582 @default.
- W4287760621 hasConcept C2778023678 @default.
- W4287760621 hasConcept C28826006 @default.
- W4287760621 hasConcept C33923547 @default.
- W4287760621 hasConcept C34388435 @default.
- W4287760621 hasConcept C39943821 @default.
- W4287760621 hasConcept C48406656 @default.
- W4287760621 hasConcept C58435881 @default.
- W4287760621 hasConceptScore W4287760621C134306372 @default.
- W4287760621 hasConceptScore W4287760621C144237770 @default.
- W4287760621 hasConceptScore W4287760621C202444582 @default.
- W4287760621 hasConceptScore W4287760621C2778023678 @default.
- W4287760621 hasConceptScore W4287760621C28826006 @default.
- W4287760621 hasConceptScore W4287760621C33923547 @default.
- W4287760621 hasConceptScore W4287760621C34388435 @default.
- W4287760621 hasConceptScore W4287760621C39943821 @default.
- W4287760621 hasConceptScore W4287760621C48406656 @default.
- W4287760621 hasConceptScore W4287760621C58435881 @default.
- W4287760621 hasLocation W42877606211 @default.
- W4287760621 hasLocation W42877606212 @default.
- W4287760621 hasLocation W42877606213 @default.
- W4287760621 hasOpenAccess W4287760621 @default.
- W4287760621 hasPrimaryLocation W42877606211 @default.
- W4287760621 hasRelatedWork W1480485137 @default.
- W4287760621 hasRelatedWork W1537069888 @default.
- W4287760621 hasRelatedWork W1608840171 @default.
- W4287760621 hasRelatedWork W1969147487 @default.
- W4287760621 hasRelatedWork W1983072522 @default.
- W4287760621 hasRelatedWork W2040425860 @default.
- W4287760621 hasRelatedWork W2947224446 @default.
- W4287760621 hasRelatedWork W3083616482 @default.
- W4287760621 hasRelatedWork W3098658947 @default.
- W4287760621 hasRelatedWork W3123844941 @default.
- W4287760621 isParatext "false" @default.
- W4287760621 isRetracted "false" @default.
- W4287760621 workType "article" @default.