The Shepp-Shiryaev Stochastic Game Driven by a Spectrally Negative Lévy Process
The Shepp-Shiryaev Stochastic Game Driven by a Spectrally Negative Lévy Process
复制标题
由谱负 Lévy 过程驱动的 Shepp-Shiryaev 随机博弈
DOI：
10.1137/s0040585x97983778
复制
发表时间：
2009
影响因子：
0.6
通讯作者：
Baurdoux E
中科院分区：
文献类型：
--
作者：
Baurdoux E
在[A. E. Kyprianou，Finance Stoch.，8（2004），pp. 73-86]，Shepp和Shiryaev的最佳停止问题的随机博弈模拟（参见。[L. A. Shepp和A. N. Shiryaev，Ann. Appl. Probab.，3（1993年），第103页。631-640]和[L. A. Shepp和A. N. Shiryaev，Theory Probab.应用程序、39（1994），第39页。103-119]）被认为是由指数布朗运动驱动时。我们考虑相同的随机博弈，我们称之为theShepp-Shiryaev随机博弈，但驱动的谱负Lévy过程和更广泛的参数范围。不像[A. E. Kyprianou，Finance Stoch.，8（2004），pp. 73-86]，我们不呼吁主要是随机分析方法。主要是，这是由于在写候选解决方案的变分不等式的帐户，然后必须与非局部积分微分算子的困难。我们呼吁，而不是一个混合的技术，包括波动理论，随机分析方法与鞅特征，减少随机游戏的最佳停止问题。
In [A. E. Kyprianou,Finance Stoch., 8 (2004), pp. 73–86], the stochastic-game-analogue of Shepp and Shiryaev's optimal stopping problem (cf. [L. A. Shepp and A. N. Shiryaev,Ann. Appl. Probab., 3 (1993), pp. 631–640] and [L. A. Shepp and A. N. Shiryaev,Theory Probab. Appl., 39 (1994), pp. 103–119]) was considered when driven by an exponential Brownian motion. We consider the same stochastic game, which we call theShepp–Shiryaev stochastic game, but driven by a spectrally negative Lévy process and for a wider parameter range. Unlike [A. E. Kyprianou,Finance Stoch., 8 (2004), pp. 73–86], we do not appeal predominantly to stochastic analytic methods. Principally, this is due to difficulties in writing down variational inequalities of candidate solutions on account of then having to work with nonlocal integro-differential operators. We appeal instead to a mixture of techniques including fluctuation theory, stochastic analytic methods associated with martingale characterizations, and reduction of the stochastic game to an optimal stopping problem.