아핀 과정의 대편차, 변환, 시뮬레이션에 관한 연구 = Large deviations, transforms, and simulations for some affine processes

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This dissertation is devoted to the study of computational aspects for some affine processes. In particular, we deal with affine diffusion processes on the canonical state space, general affine processes on positive semidefinite matrices, and a multifactor stochastic volatility model with affine property. For affine diffusion processes, we establish the sample path and finite dimensional large deviation principles. The large deviation principle is a crucial tool in asymptotic computations of probabilities of rare events, and it is recently applied to various problems in mathematical finance. Large deviation principles for some specific affine diffusion processes have been studied by some authors. We provide in this thesis a unified treatment of their large deviation results under the standard uniform topology and a mild technical condition. As the financial derivatives get complicated, the correlation and covariance between assets have become one of the most prominent sources of risks. Affine processes on positive semidefinite matrices provide a flexible and tractable family of stochastic processes for modeling realistic stochastic covariance matrices. The affine transform formula lies at the center of the computational tractability of such processes. We extend the affine transform formula from marginal distributions to linear functionals of affine processes. Moreover, we find that the transforms of brides of affine processes are closely related to marginal distributions under equivalent probability measures as well as unconditional transforms. Many empirical studies have documented that multifactor stochastic volatility models outperform single factor models in fitting term structure of implied volatilities. Among such multifactor models, the Wishart multidimensional stochastic volatility model provides most flexible features by incorporating matrix-valued Wishart process as the volatility factor. The analytic aspects of the model are well studied, but ...
Advisors
Kang, Wan-Moresearcher강완모
Description
한국과학기술원 : 수리과학과,
Publisher
한국과학기술원
Issue Date
2013
Identifier
565564/325007  / 020087004
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2013.8, [ v, 106 p. ]

Keywords

affine processes; 정확한 시뮬레이션; 변환 분석; 대편차 원리; 아핀 과정; exact simulations; large deviations; transform analysis

URI
http://hdl.handle.net/10203/197741
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=565564&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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