Matches in SemOpenAlex for { <https://semopenalex.org/work/W3100143106> ?p ?o ?g. }
Showing items 1 to 81 of
81
with 100 items per page.
- W3100143106 abstract "Geometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geometric language, the 'instantaneous arbitrage capability' generated by the market itself. The cashflow bundle is the vector bundle associated to this stochastic principal fibre bundle for the natural choice of the vector space fibre. The cashflow bundle carries a stochastic covariant differentiation induced by the connection on the principal fibre bundle. The link between arbitrage theory and spectral theory of the connection Laplacian on the vector bundle is given by the zero eigenspace resulting in a parametrization of all risk neutral measures equivalent to the statistical one. This indicates that a market satisfies the (NFLVR) condition if and only if $0$ is in the discrete spectrum of the connection Laplacian on the cash flow bundle or of the Dirac Laplacian of the twisted cash flow bundle with the exterior algebra bundle. We apply this result by extending Jarrow-Protter-Shimbo theory of asset bubbles for complete arbitrage free markets to markets not satisfying the (NFLVR). Moreover, by means of the Atiyah-Singer index theorem, we prove that the Euler characteristic of the asset nominal space is a topological obstruction to the the (NFLVR) condition, and, by means of the Bochner-Weitzenbock formula, the non vanishing of the homology group of the cash flow bundle is revealed to be a topological obstruction to (NFLVR), too. Asset bubbles are defined, classified and decomposed for markets allowing arbitrage." @default.
- W3100143106 created "2020-11-23" @default.
- W3100143106 creator A5004552611 @default.
- W3100143106 creator A5075886507 @default.
- W3100143106 date "2015-09-02" @default.
- W3100143106 modified "2023-09-27" @default.
- W3100143106 title "Can You hear the Shape of a Market? Geometric Arbitrage and Spectral Theory" @default.
- W3100143106 cites W1534181403 @default.
- W3100143106 cites W2076458153 @default.
- W3100143106 cites W2128413721 @default.
- W3100143106 cites W2157390830 @default.
- W3100143106 cites W2573293482 @default.
- W3100143106 cites W2610195475 @default.
- W3100143106 cites W3122262340 @default.
- W3100143106 cites W3125186146 @default.
- W3100143106 cites W403266949 @default.
- W3100143106 cites W2343462702 @default.
- W3100143106 doi "https://doi.org/10.48550/arxiv.1509.03264" @default.
- W3100143106 hasPublicationYear "2015" @default.
- W3100143106 type Work @default.
- W3100143106 sameAs 3100143106 @default.
- W3100143106 citedByCount "0" @default.
- W3100143106 crossrefType "posted-content" @default.
- W3100143106 hasAuthorship W3100143106A5004552611 @default.
- W3100143106 hasAuthorship W3100143106A5075886507 @default.
- W3100143106 hasBestOaLocation W31001431061 @default.
- W3100143106 hasConcept C10138342 @default.
- W3100143106 hasConcept C106953101 @default.
- W3100143106 hasConcept C114614502 @default.
- W3100143106 hasConcept C13355873 @default.
- W3100143106 hasConcept C134306372 @default.
- W3100143106 hasConcept C144947467 @default.
- W3100143106 hasConcept C159985019 @default.
- W3100143106 hasConcept C160623529 @default.
- W3100143106 hasConcept C162324750 @default.
- W3100143106 hasConcept C184720557 @default.
- W3100143106 hasConcept C191961195 @default.
- W3100143106 hasConcept C192562407 @default.
- W3100143106 hasConcept C2524010 @default.
- W3100143106 hasConcept C2778134712 @default.
- W3100143106 hasConcept C33923547 @default.
- W3100143106 hasConcept C44234333 @default.
- W3100143106 hasConcept C56907000 @default.
- W3100143106 hasConcept C66384103 @default.
- W3100143106 hasConcept C95857938 @default.
- W3100143106 hasConceptScore W3100143106C10138342 @default.
- W3100143106 hasConceptScore W3100143106C106953101 @default.
- W3100143106 hasConceptScore W3100143106C114614502 @default.
- W3100143106 hasConceptScore W3100143106C13355873 @default.
- W3100143106 hasConceptScore W3100143106C134306372 @default.
- W3100143106 hasConceptScore W3100143106C144947467 @default.
- W3100143106 hasConceptScore W3100143106C159985019 @default.
- W3100143106 hasConceptScore W3100143106C160623529 @default.
- W3100143106 hasConceptScore W3100143106C162324750 @default.
- W3100143106 hasConceptScore W3100143106C184720557 @default.
- W3100143106 hasConceptScore W3100143106C191961195 @default.
- W3100143106 hasConceptScore W3100143106C192562407 @default.
- W3100143106 hasConceptScore W3100143106C2524010 @default.
- W3100143106 hasConceptScore W3100143106C2778134712 @default.
- W3100143106 hasConceptScore W3100143106C33923547 @default.
- W3100143106 hasConceptScore W3100143106C44234333 @default.
- W3100143106 hasConceptScore W3100143106C56907000 @default.
- W3100143106 hasConceptScore W3100143106C66384103 @default.
- W3100143106 hasConceptScore W3100143106C95857938 @default.
- W3100143106 hasLocation W31001431061 @default.
- W3100143106 hasOpenAccess W3100143106 @default.
- W3100143106 hasPrimaryLocation W31001431061 @default.
- W3100143106 hasRelatedWork W2014535968 @default.
- W3100143106 hasRelatedWork W2023092859 @default.
- W3100143106 hasRelatedWork W2148197877 @default.
- W3100143106 hasRelatedWork W2740752123 @default.
- W3100143106 hasRelatedWork W2896276188 @default.
- W3100143106 hasRelatedWork W2952082998 @default.
- W3100143106 hasRelatedWork W2964063577 @default.
- W3100143106 hasRelatedWork W4297669842 @default.
- W3100143106 hasRelatedWork W4300777966 @default.
- W3100143106 hasRelatedWork W4301689072 @default.
- W3100143106 isParatext "false" @default.
- W3100143106 isRetracted "false" @default.
- W3100143106 magId "3100143106" @default.
- W3100143106 workType "article" @default.