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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2011.tde-01052013-111713
Document
Author
Full name
Alan de Genaro Dario
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2011
Supervisor
Committee
Simonis, Adilson (President)
Avellaneda, Marco Marcelo
Fernandes, Cristiano Augusto Coelho
Stern, Julio Michael
Zubelli, Jorge Passamani
Title in Portuguese
Processos de Cox com intensidade difusiva afim
Keywords in Portuguese
Difusão afim
Filtro de Kalman
Livro de Ofertas.
Processo de Cox
Abstract in Portuguese
Esta Tese explora o Processo de Cox quando sua intensidade pertence a uma família de difusões afim. A forma da funçâo densidade de Probabilidade do Processo de Cox é obtida quando a intensidade é descrita por uma difusão fim d-dimensional arbitrária. Analisa-se também o acoplamento e convergência para o Processo de Cox com intensidade afim. Para ilustrar assume-se que a intensidade do Processo é governada por uma difusão de Feller e resultados mais detalhados são obtidos. Adicionalmente, os parâmetros da intensidade do Processo são estimados por meio do Filtro de Kalman conjugado com o estimador de Quase-Máxima Verossimilhança.
Title in English
Cox Processes with Affine Intensity
Keywords in English
affine diffusion
Cox Process
Kalman Filter
Order Book.
Abstract in English
This Thesis deals with the Cox Process when its intensity belongs to a family of affine diffusions. The form of the probability density function of the Cox process is obtained when the density is described by an arbitrary d-dimensional affine diffusion. Coupling and convergence results are also addressed for a general Cox process with affine intensity. We adopted the Feller diffusion for driving the underlying intensity of the Cox Process to illustrate our results. Additionally the parameters of the underlying intensity processes are estimated by means of the Kalman Filter in conjunction with Quasi-Maximum Likelihood estimation.
 
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Tese_IME_ADG.pdf (921.50 Kbytes)
Publishing Date
2013-05-13
 
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