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Long-term factorization of the stochastic discount factor via martingale extraction
마팅게일 추출을 통한 확률할인인자의 장기적 분해

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dc.contributor.advisor박형빈-
dc.contributor.author여희준-
dc.date.accessioned2020-10-13T04:02:36Z-
dc.date.available2020-10-13T04:02:36Z-
dc.date.issued2020-
dc.identifier.other000000162707-
dc.identifier.urihttps://hdl.handle.net/10371/170706-
dc.identifier.urihttp://dcollection.snu.ac.kr/common/orgView/000000162707ko_KR
dc.description학위논문 (석사) -- 서울대학교 대학원 : 자연과학대학 수리과학부, 2020. 8. 박형빈.-
dc.description.abstractThis paper reviews the treatment of the long-term factorization of the stochastic discount factor in Qin and Linetsky (2017), and presents explicit forms of the long-term factorization in some concrete examples. The main purpose of this paper is to analyze relatively simple models in which the long-term factorization seems to be applied, so we restrict the semimartingale setting of Qin and Linetsky (2017) to rather simple one-dimensional time-homogeneous Markovian setting. Some other working models are also included as examples, though they have not been fully verifed yet. We introduce and exploit the martingale extraction method, developed by Hansen and Scheinkman (2009), as the main tool for finding the long-term factorization.-
dc.description.abstract본 논문은 Qin과 Linetsky의 확률할인인자의 장기적 분해에 대한 논의를 살펴보고 몇 가지 구체적인 예시에 대한 장기적 분해의 명확한 형태를 제시한다. 본 논문의 주요 목적은 장기적 분해가 적용될 것으로 보이는 비교적 단순한 모형들을 분석하는 것이므로, Qin과 Linetsky의 반 마팅게일 설정을 다소 간단한 1차원의 시간적으로 균등한 마르코프 설정으로 제한한다. 아직 완전히 검증되지 않은 작업 중인 몇 가지 모델들도 예시로 포함한다. Hansen과 Scheinkman이 고안한 마팅게일 추출법을 장기적 분해를 찾는 주요 도구로 소개하고 활용한다.-
dc.description.tableofcontents1 Introduction 1
2 Main tools and concepts 4
2.1 Notations, assumptions, and restrictions 4
2.2 Martingale extraction 5
2.3 Recurrence and Ergodicity 10
3 Pricing zero-coupon bond 14
3.1 Cox, Ingersoll and Ross(CIR) model 14
3.2 3/2 model 17
4 The long-term factorization 19
4.1 Preliminaries 19
4.2 Main theorems 21
4.3 Examples of models 26
4.3.1 CIR model 26
4.3.2 3/2 model 29
4.4 Some other models 31
4.4.1 Square di usion model 32
4.4.2 The inverse GARCH model 35
4.4.3 Quadratic model 37


5 Conclusion 40
Appendix A Noncentral 2-distribution and related processes 42
A.1 Noncentral 2-distributions 42
A.2 Distribution of a CIR model 44
A.3 Distribution of 3/2 model 45
Appendix B Proofs for existence and uniqueness problems 47
B.1 The square di usion model 47
B.2 The quadratic model 48
Appendix C Proofs for martingales 50
C.1 The 3/2 model 50
C.2 The inverse GARCH model 52
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dc.language.isoeng-
dc.publisher서울대학교 대학원-
dc.subjectmartingale extraction,long-term factorization,stochastic discount factor,positive eigenfunction,recurrent stochastic process-
dc.subject마팅게일 추출-
dc.subject장기적 분해-
dc.subject확률할인인자-
dc.subject양의 고유함수-
dc.subject재귀 확률과정-
dc.subject.ddc510-
dc.titleLong-term factorization of the stochastic discount factor via martingale extraction-
dc.title.alternative마팅게일 추출을 통한 확률할인인자의 장기적 분해-
dc.typeThesis-
dc.typeDissertation-
dc.contributor.department자연과학대학 수리과학부-
dc.description.degreeMaster-
dc.date.awarded2020-08-
dc.identifier.uciI804:11032-000000162707-
dc.identifier.holdings000000000043▲000000000048▲000000162707▲-
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Master's Degree_수리과학부)
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