Merton Investment Problem for the Hawkes-based Risk Model

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dc.contributor.advisorQiu, Jinniao
dc.contributor.advisorSwishchuk, Anatoliy
dc.contributor.authorNova, Mushfika Hossain
dc.contributor.committeememberBadescu, Alexandru
dc.contributor.committeememberJiang, Wenjun
dc.date2022-11
dc.date.accessioned2022-09-26T15:15:47Z
dc.date.available2022-09-26T15:15:47Z
dc.date.issued2022-09-21
dc.description.abstractWe study the Merton investment problem in insurance where the risk process is based on the general compound Hawkes process. That means the arrival of claims modeled with a Hawkes process and the modeled claim sizes follow a finite number of fixed jump sizes governed by a Markov chain evolution. The Merton investment problem in insurance is an optimal control problem and we use the dynamic programming method to derive the stochastic Hamilton-Jacobi-Bellman (SHJB) equation satisfied by the value function. The stochastic HJB equation yields a means to obtain the optimal control and thus the optimally controlled stochastic differential equation. Finally, using the claim size from the empirical data set, we simulate the optimal investment portfolio and risk process.en_US
dc.identifier.citationNova, M. H. (2022). Merton investment problem for the Hawkes-based risk model (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.en_US
dc.identifier.urihttp://hdl.handle.net/1880/115278
dc.identifier.urihttps://dx.doi.org/10.11575/PRISM/40284
dc.language.isoengen_US
dc.publisher.facultyScienceen_US
dc.publisher.institutionUniversity of Calgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.en_US
dc.subjectMerton Investment Problem in Insuranceen_US
dc.subject.classificationEducation--Mathematicsen_US
dc.titleMerton Investment Problem for the Hawkes-based Risk Modelen_US
dc.typemaster thesisen_US
thesis.degree.disciplineMathematics & Statisticsen_US
thesis.degree.grantorUniversity of Calgaryen_US
thesis.degree.nameMaster of Science (MSc)en_US
ucalgary.item.requestcopytrueen_US
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