{"id":{"repo_id":"uwo","oai_identifier":"oai:uwo.scholaris.ca:20.500.14721/37225"},"canonical_url":"https://search.dev.ndltd.org/etd/uwo/oai:uwo.scholaris.ca:20.500.14721/37225","repository":{"repo_id":"uwo","name":"Western University","base_url":"https://uwo.scholaris.ca/server/oai/request"},"display":{"title":"Modelling long-term security returns","abstract":"This research focuses on the concerns of Canadian investors regarding portfolio diversification and preparedness for unexpected risks in retirement planning. It models market crashes and two main financial instruments as independent components to simulate clients’ portfolios. Initially exploring single distributions on mutual funds such as Laplace and t distributions, the research finds limited success. Instead, a normal-Weibull spliced distribution is introduced to model log returns. The Geometric Brownian Motion (GBM) model is employed to predict and evaluate returns on common stocks using the Maximum Likelihood Estimator (MLE), assuming that daily log returns follow a normal distribution. Additionally, the Merton Jump Diffusion (MJD) model is considered to account for jumps in stock trajectories with an independent Poisson process term based on the GBM model. Market crashes, defined as a decline of at least 10% in the S&P500 over a maximum of 252 trading days, are modelled using a homogeneous Poisson process. The combined simulation results show that the model is effective in most portfolio predictions.","abstract_html":"This research focuses on the concerns of Canadian investors regarding portfolio diversification and preparedness for unexpected risks in retirement planning. It models market crashes and two main financial instruments as independent components to simulate clients’ portfolios. Initially exploring single distributions on mutual funds such as Laplace and t distributions, the research finds limited success. Instead, a normal-Weibull spliced distribution is introduced to model log returns. The Geometric Brownian Motion (GBM) model is employed to predict and evaluate returns on common stocks using the Maximum Likelihood Estimator (MLE), assuming that daily log returns follow a normal distribution. Additionally, the Merton Jump Diffusion (MJD) model is considered to account for jumps in stock trajectories with an independent Poisson process term based on the GBM model. Market crashes, defined as a decline of at least 10% in the S&P500 over a maximum of 252 trading days, are modelled using a homogeneous Poisson process. The combined simulation results show that the model is effective in most portfolio predictions.","abstract_has_math":false,"creators":["ZHU, XINGHAN"],"institution":"The University of Western Ontario","degree_name":"M Sc","degree_level":null,"degree_discipline":"Statistics and Actuarial Sciences","degree_department":null,"school":null,"contributors":[],"advisors":["Sendova, Kristina"],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-08-24","date_published":"2023-08-24","updated_at":"2026-07-27T21:56:05Z","subjects":["Spliced Distribution","Weibull Distribution","Geometric Brownian Motion","Merton Jump Diffusion","homogeneous Poisson process","market crashes"],"languages":["en_ca"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/20.500.14721/37225","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Sendova, Kristina"]},{"key":"dc:creator","label":"Author","values":["ZHU, XINGHAN"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-07-10T21:32:27Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-07-10T21:32:27Z"]},{"key":"dc:date.issued","label":"Date","values":["2023-08-24"]},{"key":"dc:publisher","label":"Institution","values":["The University of Western Ontario"]},{"key":"dc:type","label":"Dc Type","values":["thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Statistics and Actuarial Sciences"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M Sc"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Spliced Distribution","Weibull Distribution","Geometric Brownian Motion","Merton Jump Diffusion","homogeneous Poisson process","market crashes"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_ca"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/20.500.14721/37225"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Revision: Inclusion of the reference to a graph from Wikipedia","The thesis cover page in the PDF document includes references to Western University’s previous institutional repository platform, known as Scholarship@Western, and links to that platform (beginning with ir.lib.uwo.ca). In citing or referring to this thesis, use the DOI or handle from this page instead. Sample citation: Author name, \"Thesis title.\" (Year). Western University Open Repository. https://doi.org/10.71858/123456."]},{"key":"dc:description.abstract","label":"Abstract","values":["This research focuses on the concerns of Canadian investors regarding portfolio diversification and preparedness for unexpected risks in retirement planning. It models market crashes and two main financial instruments as independent components to simulate clients’ portfolios. Initially exploring single distributions on mutual funds such as Laplace and t distributions, the research finds limited success. Instead, a normal-Weibull spliced distribution is introduced to model log returns. The Geometric Brownian Motion (GBM) model is employed to predict and evaluate returns on common stocks using the Maximum Likelihood Estimator (MLE), assuming that daily log returns follow a normal distribution. Additionally, the Merton Jump Diffusion (MJD) model is considered to account for jumps in stock trajectories with an independent Poisson process term based on the GBM model. Market crashes, defined as a decline of at least 10% in the S&P500 over a maximum of 252 trading days, are modelled using a homogeneous Poisson process. The combined simulation results show that the model is effective in most portfolio predictions."]},{"key":"dc:title","label":"Title","values":["Modelling long-term security returns"]}]}],"canonical_facts":{"dc:contributor.advisor":["Sendova, Kristina"],"dc:creator":["ZHU, XINGHAN"],"dc:date.accessioned":["2025-07-10T21:32:27Z"],"dc:date.available":["2025-07-10T21:32:27Z"],"dc:date.issued":["2023-08-24"],"dc:description":["Revision: Inclusion of the reference to a graph from Wikipedia","The thesis cover page in the PDF document includes references to Western University’s previous institutional repository platform, known as Scholarship@Western, and links to that platform (beginning with ir.lib.uwo.ca). In citing or referring to this thesis, use the DOI or handle from this page instead. Sample citation: Author name, \"Thesis title.\" (Year). Western University Open Repository. https://doi.org/10.71858/123456."],"dc:description.abstract":["This research focuses on the concerns of Canadian investors regarding portfolio diversification and preparedness for unexpected risks in retirement planning. It models market crashes and two main financial instruments as independent components to simulate clients’ portfolios. Initially exploring single distributions on mutual funds such as Laplace and t distributions, the research finds limited success. Instead, a normal-Weibull spliced distribution is introduced to model log returns. The Geometric Brownian Motion (GBM) model is employed to predict and evaluate returns on common stocks using the Maximum Likelihood Estimator (MLE), assuming that daily log returns follow a normal distribution. Additionally, the Merton Jump Diffusion (MJD) model is considered to account for jumps in stock trajectories with an independent Poisson process term based on the GBM model. 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