dc.contributor.author de Jong, Klaas dc.date.accessioned 2015-09-01T22:01:09Z dc.date.available 2015-09-01T22:01:09Z dc.date.issued 2015 dc.identifier.citation de Jong, Klaas. Transient linear price impact. A second generation of market impact models.. Master thesis, University of Oslo, 2015 dc.identifier.uri http://hdl.handle.net/10852/45333 dc.description.abstract In classic mathematical finance, a trader's actions have no direct influence on the asset price. For small trades this is a reasonable assumption, but large trades fire back at the underlying price. We consider a transient linear price impact model in discrete time, and find a deterministic and unique optimal trading strategy when the decay of price impact is given as a positive-definite quadratic form. Examples of the associated so-called resilience functions show a new type of price manipulation, which will be called transaction-triggered price manipulation. To exclude this kind of price manipulation, convexity of the resilience function appears to be both necessary and sufficient. Since nonconstant, convex functions generate positive definite quadratic forms, standard price manipulation is excluded in this case as well. The effects of risk aversion can be handled similarly to the way the standard optimal order execution problem is solved. The discrete-time model can be extended to continuous time, and we find some similar results. It appears that optimal strategies can be characterized as measure-valued solutions of a generalized Fredholm integral equation of the first kind. However, to guarantee the existence of an optimal trading strategy, positive definiteness does not hold, and we need convexity of the decay kernel. As in the discrete-time case, this excludes the existence of transaction-triggered price manipulation strategies. eng dc.language.iso eng dc.subject market dc.subject impact dc.subject model dc.subject transient dc.subject price dc.subject impact dc.subject optimal dc.subject order dc.subject execution dc.subject positive dc.subject semi dc.subject definite dc.subject quadratic dc.subject form dc.subject price dc.subject manipulation dc.subject Lagrange dc.subject multiplier dc.subject Bochner dc.subject s dc.subject theorem dc.subject Fourier dc.subject transform dc.subject convex dc.subject function dc.subject Lebesgue dc.subject Stieltjes dc.subject measure dc.subject Lebesgue dc.subject Stieltjes dc.subject integral dc.subject integration dc.subject by dc.subject parts dc.subject for dc.subject Lebesgue dc.subject Stieltjes dc.subject integrals dc.subject dominated dc.subject convergence dc.subject continuity dc.subject theorem dc.subject portmanteau dc.subject theorem dc.subject Fubini dc.subject Tonelli dc.subject theorem dc.subject transaction dc.subject triggered dc.subject price dc.subject manipulation dc.subject risk dc.subject aversion dc.subject bilinear dc.subject form dc.subject polarization dc.subject Fredholm dc.subject integral dc.subject equation dc.subject Borel dc.subject probability dc.subject measure dc.subject compact dc.subject metric dc.subject space dc.subject Prohorov dc.subject s dc.subject theorem dc.title Transient linear price impact. A second generation of market impact models. eng dc.type Master thesis dc.date.updated 2015-09-01T22:01:09Z dc.creator.author de Jong, Klaas dc.identifier.urn URN:NBN:no-49536 dc.type.document Masteroppgave dc.identifier.fulltext Fulltext https://www.duo.uio.no/bitstream/handle/10852/45333/1/MasterThesis_KlaasdeJong.pdf
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