کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
978900 | 933309 | 2010 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The application of fractional derivatives in stochastic models driven by fractional Brownian motion
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In this paper, in order to establish connection between fractional derivative and fractional Brownian motion (FBM), we first prove the validity of the fractional Taylor formula proposed by Guy Jumarie. Then, by using the properties of this Taylor formula, we derive a fractional Itô formula for H∈[1/2,1)H∈[1/2,1), which coincides in form with the one proposed by Duncan for some special cases, whose formula is based on the Wick Product. Lastly, we apply this fractional Itô formula to the option pricing problem when the underlying of the option contract is supposed to be driven by a geometric fractional Brownian motion. The case that the drift, volatility and risk-free interest rate are all dependent on tt is also discussed.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica A: Statistical Mechanics and its Applications - Volume 389, Issue 21, 1 November 2010, Pages 4809–4818
Journal: Physica A: Statistical Mechanics and its Applications - Volume 389, Issue 21, 1 November 2010, Pages 4809–4818
نویسندگان
Lv Longjin, Fu-Yao Ren, Wei-Yuan Qiu,