Series Expansions for the First Passage Distribution of Wong-Pearson Jump-Diffusions
Series Expansions for the First Passage Distribution of Wong-Pearson Jump-Diffusions
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DOI：
10.1080/07362990902976611
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发表时间：
2009-01-01
影响因子：
1.3
通讯作者：
Rabehasaina, Landy
中科院分区：
文献类型：
--
作者：
Avram, Florin;Leonenko, Nikolai;Rabehasaina, Landy
我们探讨了一类特殊的跳跃扩散多项式状态依赖系数的第一次通过问题的厄兰级数方法。这种方法可以被视为拉普拉斯变换的离散模拟，它通过代数递归来替换具有该函数满足的多项式系数的微分方程。我们确定的情况下，其中的扩展是有限的，并在其中的复发是二阶，从而更容易解决。
We explore the Erlang series approach for the first-time passage problem for a particular class of jump-diffusions with polynomial state-dependent coefficients. This approach may be viewed as a discrete analog of the Laplace transform, which replaces the differential equations with polynomial coefficients satisfied by this function by algebraic recurrences. We identify cases in which the expansion is finite and in which the recurrence is of second order, and thus more easily solved.