Otimização estocástica de portfólio
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional do FGV (FGV Repositório Digital) |
Texto Completo: | http://hdl.handle.net/10438/16969 |
Resumo: | In Øksendal (1998), we can see the derivation of a classical stochastic optimization between an asset, or a class of assets, risky and other risk-free. But, after the decision of which portion of the resources to allocate in the risky investment class, questions arise about how would the division of the resources between the assets that comprise it. We assume that some investor choose to invest in two risky assets and, following the classic studies of portfolio stochastic optimization, mainly by Øksendal, the proposal is to introduce a new technique of trading consisting in recurrent rebalancing approach stochastic optimization investments with risk. Following the short-term concept provided by Ang, Hodrick, Xing and Zhang (2006) for the stock market, it was considered a sequence of short rebalancing time horizons and, at the beginning of each period, the parameters are recalculated and a new optimal control is established. By adopting this technique, the volatilities of the assets constituting the portfolio are recalculated and, therefore, it is a proxy to solution of the heteroscedasticity problem. Also noteworthy, being something new in literature, the fact of having been derived from an optimal control for a portfolio containing two investments with risk. The stochastic optimization procedure was similar to that adopted by Øksendal, namely, the application of the Hamilton-Jacobi-Bellman theorem to transform the problem of minimizing the cost functional a partial differential equation known as HJB equation, in reference to the authors. The steps followed by Øksenal are the same for us, from the optimization’s point of view, and are well summarized by Ross (2008). |
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Pereira, Yuri Marques MedeirosEscolas::EESPBotelho, MarcosYoneyama, TakashiPinto, Afonso de Campos2016-09-01T19:33:44Z2016-09-01T19:33:44Z2016-08-05PEREIRA, Yuri Marques Medeiros. Otimização estocástica de portfólio. Dissertação (Mestrado Profissional em Finanças e Economia) - FGV - Fundação Getúlio Vargas, São Paulo, 2016.http://hdl.handle.net/10438/16969In Øksendal (1998), we can see the derivation of a classical stochastic optimization between an asset, or a class of assets, risky and other risk-free. But, after the decision of which portion of the resources to allocate in the risky investment class, questions arise about how would the division of the resources between the assets that comprise it. We assume that some investor choose to invest in two risky assets and, following the classic studies of portfolio stochastic optimization, mainly by Øksendal, the proposal is to introduce a new technique of trading consisting in recurrent rebalancing approach stochastic optimization investments with risk. Following the short-term concept provided by Ang, Hodrick, Xing and Zhang (2006) for the stock market, it was considered a sequence of short rebalancing time horizons and, at the beginning of each period, the parameters are recalculated and a new optimal control is established. By adopting this technique, the volatilities of the assets constituting the portfolio are recalculated and, therefore, it is a proxy to solution of the heteroscedasticity problem. Also noteworthy, being something new in literature, the fact of having been derived from an optimal control for a portfolio containing two investments with risk. The stochastic optimization procedure was similar to that adopted by Øksendal, namely, the application of the Hamilton-Jacobi-Bellman theorem to transform the problem of minimizing the cost functional a partial differential equation known as HJB equation, in reference to the authors. The steps followed by Øksenal are the same for us, from the optimization’s point of view, and are well summarized by Ross (2008).Em Øksendal (1998), podemos ver a derivação de um modelo clássico de otimização estocástica entre um ativo, ou classe de ativos, com risco e outro sem risco. Mas, após a decisão do quanto alocar na classe de investimento com risco, ficou o questionamento sobre como ficaria a divisão dos recursos entre os ativos que a compõem. Partimos do princípio que determinado investidor optou por escolher investir em dois ativos com risco e, seguindo os estudos clássicos de otimização estocástica de portfólio, principalmente o promovido por Øksendal, a proposta é apresentar uma nova técnica de trading que consiste na abordagem de rebalanceamentos sucessivos por otimização estocástica em investimentos com risco. Seguindo a noção de curto prazo fornecida por Ang, Hodrick, Xing e Zhang (2006) para o mercado de ações, foi considerada uma sequência de horizontes curtos de rebalanceamento e, ao início de cada período, os parâmetros são recalculados e um novo controle ótimo é estabelecido. Ao adotar esta técnica, as volatilidades dos ativos que constituem o portfólio são recalculadas e, com isso, diminui-se o problema de heterocedasticidade. Também merece destaque, por ser algo novo na literatura, o fato de ter sido derivado um controle ótimo para um portfólio que contém dois investimentos com risco. O procedimento de otimização estocástica foi similar ao adotado por Øksendal, qual seja, a aplicação do teorema de Hamilton-Jacobi-Bellman para transformar o problema de minimização da funcional custo numa equação diferencial parcial conhecida como equação HJB, em referência aos autores. Os passos seguidos por Øksenal e por nós serão os mesmos, do ponto de vista de otimização, e estão bem resumidos por Ross (2008).porControle estocásticoOtimização de portfólioEquação de Hamilton-Jacobi-Bellman (HJB)Função utilidadeBalanceamento de investimentos com riscoRebalanceamentos sucessivosFundos de índice (ETF)EconomiaProcesso estocásticoInvestimentosAdministração de riscoOtimização estocástica de portfólioinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisreponame:Repositório Institucional do FGV (FGV Repositório Digital)instname:Fundação Getulio Vargas (FGV)instacron:FGVinfo:eu-repo/semantics/openAccessTEXTDissertação YURI PEREIRA.pdf.txtDissertação YURI PEREIRA.pdf.txtExtracted texttext/plain82096https://repositorio.fgv.br/bitstreams/6e65e0b1-e6d7-412a-8942-d9edfda16e05/downloadc542f60a35b6618c3851e3212787c402MD57ORIGINALDissertação YURI PEREIRA.pdfDissertação YURI 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|
dc.title.por.fl_str_mv |
Otimização estocástica de portfólio |
title |
Otimização estocástica de portfólio |
spellingShingle |
Otimização estocástica de portfólio Pereira, Yuri Marques Medeiros Controle estocástico Otimização de portfólio Equação de Hamilton-Jacobi-Bellman (HJB) Função utilidade Balanceamento de investimentos com risco Rebalanceamentos sucessivos Fundos de índice (ETF) Economia Processo estocástico Investimentos Administração de risco |
title_short |
Otimização estocástica de portfólio |
title_full |
Otimização estocástica de portfólio |
title_fullStr |
Otimização estocástica de portfólio |
title_full_unstemmed |
Otimização estocástica de portfólio |
title_sort |
Otimização estocástica de portfólio |
author |
Pereira, Yuri Marques Medeiros |
author_facet |
Pereira, Yuri Marques Medeiros |
author_role |
author |
dc.contributor.unidadefgv.por.fl_str_mv |
Escolas::EESP |
dc.contributor.member.none.fl_str_mv |
Botelho, Marcos Yoneyama, Takashi |
dc.contributor.author.fl_str_mv |
Pereira, Yuri Marques Medeiros |
dc.contributor.advisor1.fl_str_mv |
Pinto, Afonso de Campos |
contributor_str_mv |
Pinto, Afonso de Campos |
dc.subject.por.fl_str_mv |
Controle estocástico Otimização de portfólio Equação de Hamilton-Jacobi-Bellman (HJB) Função utilidade Balanceamento de investimentos com risco Rebalanceamentos sucessivos Fundos de índice (ETF) |
topic |
Controle estocástico Otimização de portfólio Equação de Hamilton-Jacobi-Bellman (HJB) Função utilidade Balanceamento de investimentos com risco Rebalanceamentos sucessivos Fundos de índice (ETF) Economia Processo estocástico Investimentos Administração de risco |
dc.subject.area.por.fl_str_mv |
Economia |
dc.subject.bibliodata.por.fl_str_mv |
Processo estocástico Investimentos Administração de risco |
description |
In Øksendal (1998), we can see the derivation of a classical stochastic optimization between an asset, or a class of assets, risky and other risk-free. But, after the decision of which portion of the resources to allocate in the risky investment class, questions arise about how would the division of the resources between the assets that comprise it. We assume that some investor choose to invest in two risky assets and, following the classic studies of portfolio stochastic optimization, mainly by Øksendal, the proposal is to introduce a new technique of trading consisting in recurrent rebalancing approach stochastic optimization investments with risk. Following the short-term concept provided by Ang, Hodrick, Xing and Zhang (2006) for the stock market, it was considered a sequence of short rebalancing time horizons and, at the beginning of each period, the parameters are recalculated and a new optimal control is established. By adopting this technique, the volatilities of the assets constituting the portfolio are recalculated and, therefore, it is a proxy to solution of the heteroscedasticity problem. Also noteworthy, being something new in literature, the fact of having been derived from an optimal control for a portfolio containing two investments with risk. The stochastic optimization procedure was similar to that adopted by Øksendal, namely, the application of the Hamilton-Jacobi-Bellman theorem to transform the problem of minimizing the cost functional a partial differential equation known as HJB equation, in reference to the authors. The steps followed by Øksenal are the same for us, from the optimization’s point of view, and are well summarized by Ross (2008). |
publishDate |
2016 |
dc.date.accessioned.fl_str_mv |
2016-09-01T19:33:44Z |
dc.date.available.fl_str_mv |
2016-09-01T19:33:44Z |
dc.date.issued.fl_str_mv |
2016-08-05 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
PEREIRA, Yuri Marques Medeiros. Otimização estocástica de portfólio. Dissertação (Mestrado Profissional em Finanças e Economia) - FGV - Fundação Getúlio Vargas, São Paulo, 2016. |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10438/16969 |
identifier_str_mv |
PEREIRA, Yuri Marques Medeiros. Otimização estocástica de portfólio. Dissertação (Mestrado Profissional em Finanças e Economia) - FGV - Fundação Getúlio Vargas, São Paulo, 2016. |
url |
http://hdl.handle.net/10438/16969 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
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Fundação Getulio Vargas (FGV) |
instacron_str |
FGV |
institution |
FGV |
reponame_str |
Repositório Institucional do FGV (FGV Repositório Digital) |
collection |
Repositório Institucional do FGV (FGV Repositório Digital) |
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MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional do FGV (FGV Repositório Digital) - Fundação Getulio Vargas (FGV) |
repository.mail.fl_str_mv |
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