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dc.contributor.advisorKruse, Thomas
dc.contributor.authorAckermann, Julia
dc.date.accessioned2023-03-29T10:44:20Z
dc.date.available2023-03-29T10:44:20Z
dc.date.issued2022-11
dc.identifier.urihttps://jlupub.ub.uni-giessen.de//handle/jlupub/16166
dc.identifier.urihttp://dx.doi.org/10.22029/jlupub-15548
dc.description.abstractWe analyze linear-quadratic (LQ) stochastic control problems that arise in optimal trade execution in models of Obizhaeva-Wang type. Extending previous literature, order book depth and resilience are both allowed to be stochastic processes. Moreover, the target position can be a random variable, and we can include a risk term with stochastic target process. In discrete time, we tind via the dynamic programming principle that the optimal trade sizes and the minimal costs are characterized by a process Y, which is defined by backward recursion, and by, for general targets, a further process ψ. We moreover investigate properties of our model such as savings in the long-time horizon, existence of profitable round trips, and premature closure of the position. In continuous time, we go beyond the usual finite-variation strategies, and present two approaches. In the first one, we set up and solve a relevant control problem where we consider càdlàg semimartingales as execution strategies, while in the second one, we start from a typical formulation for finite-variation strategies, extend this continuously to progressively measurable strategies, and solve the extended problem via reduction to a standard LQ stochastic control problem and subsequent application of relevant literature. The counterpart of the process Y from discrete time now is the solution of a quadratic backward stochastic differential equation (BSDE), and ψ becomes the solution of a linear BSDE. It turns out that optimal strategies indeed can have infinite variation.de_DE
dc.language.isoende_DE
dc.rightsIn Copyright*
dc.rights.urihttp://rightsstatements.org/page/InC/1.0/*
dc.subject.ddcddc:510de_DE
dc.titleAnalysis of linear-quadratic optimization problems for semimartingales and application in optimal trade executionde_DE
dc.typedoctoralThesisde_DE
dcterms.dateAccepted2023-03-21
local.affiliationFB 07 - Mathematik und Informatik, Physik, Geographiede_DE
thesis.levelthesis.doctoralde_DE


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