共查询到19条相似文献,搜索用时 109 毫秒
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《数学的实践与认识》2015,(20)
假设标的资产由混合分数布朗运动驱动,利用分数It6公式得到了混合分数布朗运动环境下永久美式期权的Black-Scholes偏微分方程,并通过偏微分方程获得永久美式期权的定价公式. 相似文献
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在等价鞅测度下,研究标的资产价格服从几何分数布朗运动的幂期权看涨、看跌定价公式及其平价公式.并与基于标准布朗运动的幂期权定价公式进行比较分析,进一步论证布朗运动只是分数布朗运动的一种特例,可基于分数布朗运动对原有的期权定价模型进行推广. 相似文献
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混合分数布朗运动下亚式期权定价 总被引:2,自引:0,他引:2
运用混合分数布朗运动的Ito公式,将几何平均亚式期权定价化成一个偏微分方程求解问题,通过偏微分方程求解获得了几何平均型亚式看涨期权的定价公式. 相似文献
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假设股票价格变化过程服从几何分数布朗运动,建立了分数布朗运动下的亚式期权定价模型.利用分数-It-公式,推导出分数布朗运动下亚式期权的价值所满足的含有三个变量偏微分方程.然后,引进适当的组合变量,将其定解问题转化为一个与路径无关的一维微分方程问题.进一步通过随机偏微分方程方法求解出分数布朗运动下亚式期权的定价公式.最后利用权证定价原理对稀释效用做出调整后,得到分数布朗运动下亚式股本权证定价公式.<正>~~ 相似文献
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Anne MacKay Alexander Melnikov 《Stochastics An International Journal of Probability and Stochastic Processes》2018,90(7):1087-1110
In this paper, we investigate two-sided bounds for the small ball probability of a mixed fractional Brownian motion with a general deterministic trend function, in terms of respective small ball probability of a mixed fractional Brownian motion without trend. To maximize the lower bound, we consider various ways to split the trend function between the components of the mixed fractional Brownian motion for the application of Girsanov theorem, and we show that the optimal split is the solution of a Fredholm integral equation. We find that the upper bound for the probability is also a function of this optimal split. The asymptotic behaviour of the probability as the ball becomes small is analysed for zero trend function and for the particular choice of the upper limiting function. 相似文献
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本文给出了由两个不同的分数布朗运动组成的重分数布朗运动的Strassen型泛函重对数律和局部Strassen型泛函重对数律.我们的结果也适用于由两个布朗运动组成的重布朗运动及由一个分数布朗运动和一个布朗运动组成的重过程.最后将上述结果推广到n重分数布朗运动中.推广了已有文献的相应结果. 相似文献
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We define and prove the existence of a fractional Brownian motion indexed by a collection of closed subsets of a measure space.
This process is a generalization of the set-indexed Brownian motion, when the condition of independance is relaxed. Relations
with the Lévy fractional Brownian motion and with the fractional Brownian sheet are studied. We prove stationarity of the
increments and a property of self-similarity with respect to the action of solid motions. Moreover, we show that there no
“really nice” set indexed fractional Brownian motion other than set-indexed Brownian motion. Finally, behavior of the set-indexed
fractional Brownian motion along increasing paths is analysed.
相似文献
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本文研究混合分数O-U过程的最小范数估计问题.利用分数布朗运动驱动的随机微分方程偏差不等式,获得了混合分数O-U过程漂移参数的最小范数估计、相合性及渐近分布. 相似文献
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Tempered fractional Brownian motion is obtained when the power law kernel in the moving average representation of a fractional Brownian motion is multiplied by an exponential tempering factor. This paper develops the theory of stochastic integrals for tempered fractional Brownian motion. Along the way, we develop some basic results on tempered fractional calculus. 相似文献
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We study a mixed financial market with risky asset governed by both the standard Brownian motion and the fractional Brownian
motion with Hurst index
H ? (\frac12, 1){H\in(\frac12, 1)}. We use representations of Hitsuda and Cheridito for the mixed Brownian and fractional Brownian process and present the solution
of the problem of efficient hedging for
H ? (\frac34, 1){H\in(\frac34, 1)}. To solve the problem for
H ? (\frac12, 1){H\in(\frac12, 1)} and to avoid some computational difficulties, we introduce the approximate incomplete semimartingale market, and the solution
of the approximate problem of efficient hedging is considered. Then we pass to the limit and observe the asymptotic behavior
of the solution of the efficient hedging problem. 相似文献
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Journal of Theoretical Probability - In this paper, we explore the generalized mixed fractional Brownian motion in the set-indexed framework and generalize several recent results from Miao et al.... 相似文献
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The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-field Stochastic Differential Equations 下载免费PDF全文
In this paper, some properties of a stochastic convolution driven by tempered fractional Brownian motion are obtained. Based on this result, we get the existence and uniqueness of stochastic mean-field equation driven by tempered fractional Brownian motion. Furthermore, combining with the Banach fixed point theorem and the properties of Mittag-Leffler functions, we study the existence and uniqueness of mild solution for a kind of time fractional mean-field stochastic differential equation driven by tempered fractional Brownian motion. 相似文献