{"id":{"repo_id":"calgary","oai_identifier":"oai:ucalgary.scholaris.ca:1880/115278"},"canonical_url":"https://search.dev.ndltd.org/etd/calgary/oai:ucalgary.scholaris.ca:1880/115278","repository":{"repo_id":"calgary","name":"University of Calgary","base_url":"https://ucalgary.scholaris.ca/server/oai/request"},"display":{"title":"Merton Investment Problem for the Hawkes-based Risk Model","abstract":"We 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.","abstract_html":"We 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.","abstract_has_math":false,"creators":["Nova, Mushfika Hossain"],"institution":"Science","degree_name":"Master of Science (MSc)","degree_level":null,"degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":[],"advisors":["Qiu, Jinniao","Swishchuk, Anatoliy"],"committee_chairs":[],"committee_members":["Badescu, Alexandru","Jiang, Wenjun"],"year":2022,"date_issued":"2022-09-21","date_published":"2022-09-21","updated_at":"2026-07-24T01:30:42Z","subjects":["Merton Investment Problem in Insurance"],"languages":["eng"],"rights":["University 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."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://dx.doi.org/10.11575/PRISM/40284"],"render_values":[{"text":"https://dx.doi.org/10.11575/PRISM/40284","href":"https://dx.doi.org/10.11575/PRISM/40284","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1880/115278","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Qiu, Jinniao","Swishchuk, Anatoliy"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Badescu, Alexandru","Jiang, Wenjun"]},{"key":"dc:creator","label":"Author","values":["Nova, Mushfika Hossain"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-11"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2022-09-26T15:15:47Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-09-26T15:15:47Z"]},{"key":"dc:date.issued","label":"Date","values":["2022-09-21"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Calgary"]},{"key":"dc:type","label":"Dc Type","values":["master thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics & Statistics"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MSc)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Calgary"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Merton Investment Problem in Insurance"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["University 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."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://dx.doi.org/10.11575/PRISM/40284"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1880/115278"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We 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."]},{"key":"dc:title","label":"Title","values":["Merton Investment Problem for the Hawkes-based Risk Model"]}]}],"canonical_facts":{"dc:contributor.advisor":["Qiu, Jinniao","Swishchuk, Anatoliy"],"dc:contributor.committeemember":["Badescu, Alexandru","Jiang, Wenjun"],"dc:creator":["Nova, Mushfika Hossain"],"dc:date":["2022-11"],"dc:date.accessioned":["2022-09-26T15:15:47Z"],"dc:date.available":["2022-09-26T15:15:47Z"],"dc:date.issued":["2022-09-21"],"dc:description.abstract":["We 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."],"dc:identifier.doi":["https://dx.doi.org/10.11575/PRISM/40284"],"dc:identifier.uri":["http://hdl.handle.net/1880/115278"],"dc:language.iso":["eng"],"dc:publisher.institution":["University of Calgary"],"dc:rights":["University 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."],"dc:subject":["Merton Investment Problem in Insurance"],"dc:title":["Merton Investment Problem for the Hawkes-based Risk Model"],"dc:type":["master thesis"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_name":["Master of Science (MSc)"],"thesis:institution_name":["University of Calgary"]},"updated_at":"2026-07-24T01:30:42Z"}