Limitations of dynamic programming approach: singularity and time inconsistency

dc.contributor.advisor Goldys, Beniamin en_US
dc.contributor.advisor Penev, Spiridon en_US Wu, Wei en_US 2022-03-15T11:17:12Z 2022-03-15T11:17:12Z 2016 en_US
dc.description.abstract Two failures of the dynamic programming (DP) approach to the stochastic optimal control problem are investigated. The first failure arises when we wish to solve a class of certain singular stochastic control problems in continuous time. It has been shown by Lasry and Lions (2000) that this difficulty can be overcome by introducing equivalent standard stochastic control problems. To solve this class of singular stochastic control problems, it remains to solve the equivalent standard stochastic control problems. Since standard stochastic control problems can be solved by applying the DP approach, this then solves the first failure. In the first part of the thesis, we clarify the idea of Lasry and Lions and extend their work to the case of controlled processes with jumps. This is particularly important in financial modelling where such processes are widely applied. For the purpose of application, we applied our result to an optimal trade execution problem studied by Lasry and Lions (2007b). The second failure of the DP approach arises when we wish to solve a multiperiod portfolio selection problem in which a mean-standard-deviation type criterion (a non-separable criterion) is used. We formulate such a problem as a discrete time stochastic control problem. By adapting a pseudo dynamic programming principle, we obtain a closed form optimal strategy for investors whose risk tolerances are larger than a lower bound. As a consequence, we develop a multiperiod portfolio selection scheme. The analysis is performed in the market of risky assets only, however, we allow both market transitions and intermediate cash injections and offtakes. This work provides a good basis for future studies of portfolio selection problems with selection criteria chosen from the class of translation-invariant and positive-homogeneous risk measures. en_US
dc.language English
dc.language.iso EN en_US
dc.publisher UNSW, Sydney en_US
dc.rights CC BY-NC-ND 3.0 en_US
dc.rights.uri en_US
dc.subject.other Stochastic optimal control. en_US
dc.subject.other Dynamic programming. en_US
dc.subject.other Stochastic control. en_US
dc.title Limitations of dynamic programming approach: singularity and time inconsistency en_US
dc.type Thesis en_US
dcterms.accessRights open access
dcterms.rightsHolder Wu, Wei
dspace.entity.type Publication en_US
unsw.accessRights.uri 2018-07-30 en_US
unsw.description.embargoNote Embargoed until 2018-07-30
unsw.relation.faculty Science
unsw.relation.originalPublicationAffiliation Wu, Wei, Mathematics & Statistics, Faculty of Science, UNSW en_US
unsw.relation.originalPublicationAffiliation Goldys, Beniamin, The University of Sydney en_US
unsw.relation.originalPublicationAffiliation Penev, Spiridon , Mathematics & Statistics, Faculty of Science, UNSW en_US School of Mathematics & Statistics *
unsw.thesis.degreetype PhD Doctorate en_US
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