山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (4): 36-41.doi: 10.6040/j.issn.1671-9352.2.2017.156
陈丽,林玲*
CHEN Li, LIN Ling*
摘要： 主要研究标的股票价格满足随机微分延迟方程(stochastic differential delay equation, SDDE)时欧式期权的定价公式,采用倒向随机微分方程(backward stochastic differential equation, BSDE)方法进行处理,值得注意的是得到的财富方程与经典的BSDE有差异,该方程为时滞BSDE。利用时滞BSDE与超前随机微分方程(advanced stochastic differential equations, ASDE)的对偶关系,给出股票价格具有时滞的欧式看涨期权的定价公式。
中图分类号:
| [1] COOTNER P H. The random character of stock market prices[M]. Cambridge: MIT Press, 1964. [2] MERTON R C. Theory of rational option pricing[J]. The Bell Journal of Economics and Management Science, 1973, 4(1):141-183. [3] MERTON R C. Continuous-time finance[M]. Oxford: Basil Blackwell, 1990. [4] SCOTT L. Option pricing when the variance changes randomly: theory, estimation and an application[J]. Journal of Financial and Quantitative Analysis, 1987, 22(4):419-438. [5] RUBINSTEIN M. Implied binomial trees[J]. Journal of Finance, 1994, 49(3):771-818. [6] HU Yaozhong, ØKSENDAL B. Fractional white noise calculus and applications to finance[J]. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2003, 6(1):1-32. [7] SCHOENMAKERS J, KLOEDEN P. Robust option replication for a black and scholes model extended with nondeterministic trends[J]. Journal of Applied Mathematics and Stochastic Analysis, 1999, 12(2):113-120. [8] ARRIOJAS M, HU Yaozhong, MOHAMMED S E, et al. A delayed black and scholes formula[J]. Stochastic Analysis and Applications, 2007, 25:471-492. [9] KAZMERCHUK Y, SWISHCHUK A, WU Jianhong. The pricing of option for securities markets with delayed response[J]. Mathematics and Computers Simulation, 2007, 75:69-79. [10] BISMUT J M. An introductory approach to duality in optimal stochastic control[J]. SIAM Review, 1978, 20(1):62-78. [11] PARDOUX E, PENG Shige. Adapted solution of a backward stochastic differential equation[J]. Systems Control Lett, 1990, 14:55-61. [12] DUFFIE D, EPSTEIN L G. Stochastic differential utility[J]. Econometrica, 1992, 60(2):353-394. [13] DELONG Ł, IMKELLER P. Backward stochastic differential equations with time delayed generatorsresults and counterexamples[J]. Annals of Applied Probability, 2010, 20(4):1512-1536. [14] MOHAMMED SE A. Stochastic functional differential equations[M]. Boston: Pitman Advanced Publishing Program, 1984. [15] MOHAMMED SE A. Stochastic differential equations with memory: theory, examples and applications[J]. Progress in Probability, 1996, 42:1-77. [16] CHEN Li, HUANG Jianhui. Stochastic maximum principle for controlled backward delayed system via advanced stochastic differential equation[J]. Journal of Optimization Theory and Applications, 2015, 167(3):1112-1135. [17] DELONG Ł. Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management[J]. Quantitative Finance, 2010, 20(3):333-418. [18] SHI Jingtao, WANG Guangchen. A non-zero sum differential game of BSDE with time-delayed generator and applications[J]. IEEE Transactions on Automatic Control, 2016, 61(7):1959-1964. [19] ØKSENDAl B. Stochastic differential equations: an introduction with applications[M]. Berlin: Springer, 2003. |
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