On the Monitoring Error of the Supremum of a Normal Jump Diffusion Process
On the Monitoring Error of the Supremum of a Normal Jump Diffusion Process
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正常跳跃扩散过程上界的监测误差
DOI：
10.1239/jap/1324046016
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发表时间：
2011
影响因子：
1
通讯作者：
R. Song
中科院分区：
文献类型：
--
作者：
Ao Chen;Liming Feng;R. Song
我们得出了连续监视的超级范围之间（预期）差的扩展，甚至在跳跃差异过程的有限时间范围内监视了离散的最大值，并具有独立且相同分布的正常跳跃尺寸。 1/2 + a 1/n 3/2 +··· + b 1/n + b 2/n 2 + b 4/n 4 +···，其中n是监视间隔的数量。对于系数{a 0，a 1，…，b 1，b 2，尤其运动概率和数学金融中的运动。
We derive an expansion for the (expected) difference between the continuously monitored supremum and evenly monitored discrete maximum over a finite time horizon of a jump diffusion process with independent and identically distributed normal jump sizes. The monitoring error is of the form a 0 / N 1/2 + a 1 / N 3/2 + · · · + b 1 / N + b 2 / N 2 + b 4 / N 4 + · · ·, where N is the number of monitoring intervals. We obtain explicit expressions for the coefficients {a 0, a 1, …, b 1, b 2, …}. In particular, a 0 is proportional to the value of the Riemann zeta function at ½, a well-known fact that has been observed for Brownian motion in applied probability and mathematical finance.