博碩士論文 87221002 詳細資訊


姓名 盧楓旻( Feng-Ming Ru)  查詢紙本館藏   畢業系所 數學系
論文名稱 不完整市場的亞洲選擇權
(Incomplete market Asian options)
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摘要(中) 在第一節中,我們得到了含有一次跳躍的亞式選擇權的封閉解。在第二節中,我們建立了含有Poisson跳躍的亞式選擇權與二階微分方程的關係;並且我們也得到了含有多重跳躍的亞式選擇權的計價方法。
摘要(英) relation between a second order differential equation and the Asian option with Poisson-jump. At last we also develope a formula of
pricing the Asian option with multi-jump.
關鍵字(中) ★ 不完整市場
★ 亞洲選擇權
★ 馬可夫過程
關鍵字(英) ★ Incomplete market
★ asian option
★ Markov process
論文目次 0 Introduction...........................................0
1 Asian option with one jump.............................4
1-1 Dynamics of the underlying asset and pricing........4
1-2 Application to Calls................................7
1-3 Application to Puts................................26
2 Asian option with multi-jump..........................28
2-1 The Dynamic of the underlying asset and differ-
ential equation...................................28
2-2 Pricing............................................37
3 Reference.............................................41
參考文獻 [1] de Hann,L. and Karandikar,R.L.:Embedding a stochastic difference equation into a continuous-time process. Stochastic Processes and their Applications.32
[2] Exton,H., ed. :Multiple Hypergeometric Functions and Applications. Ellis Horwood Limited, 1976.
[3] Exton,H., ed. :Handbook of Hypergeometric Integrals. Ellis Horwood Limited, 1978.
[4] Kwok.Y.K.: Mathematical Models of Financial Derivatives.Springer-Verlag, 1998.
[5] Lamberton,D. and Lapeyre,B.: Introduction to Stochastic Calculus Applied to Finance. Chapman and Hall, 1996.
[6] Lebedev,N.N. :Special Functions and Their Applications.Dover Publications, 1972.
[7] Merton,R.C. :Theory of rational option pricing. Bell Jornal of Economics and Management Sciences, vol.4,1973.
pp.141-183.
[8] Protter,P. :Stochastic Integration and Differential Equations. Springer-Verlag, Berlin Heidelberg, 1990.
[9] Revuz,A. and Yor,M. :Continuous Martingales and Brownian Motion. Springer-Verlag, 1991.
[10]
Yor,M. :Some Aspects of Brownian Motion. Part I : Some Special Functionals.}Lectures in Mathematics. ETH Z"{u}rich,
Birkh"{a}user, 1992.
[11] Yor,M., ed.: Exponential functionals and pricipal values related to Brownian motion. Biblioteca de la Revista
Matematica Ibero-Americana, 1997.
[12] Yor,M. :Some Aspects of Brownian Motion. Part II : Some Recent Martingale Problems. Lectures in Mathematics. ETH Z"{u}rich, Birkh"{a}user, 1997.
[13] Yor,M., ed.: On certain Markov processes attached to exponential functionals of Brownian motion ; application to Asian options. To appear in Revista Matematica Iberoamericana.(2001).
指導教授 周青松(Ching-Sung Chou) 審核日期 2001-7-9
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