Discounted Optimal Stopping for Maxima of Some Jump-Diffusion Processes
Discounted Optimal Stopping for Maxima of Some Jump-Diffusion Processes
复制标题
某些跳跃扩散过程的最大值的贴现最优停止
DOI：
10.1239/jap/1189717540
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发表时间：
2007
影响因子：
1
通讯作者：
P. Gapeev
中科院分区：
文献类型：
--
作者：
P. Gapeev
本文给出了一类由布朗运动和带指数跳的复合Poisson过程驱动的模型中最大值过程的折扣最优停时问题的封闭解。证明的方法是基于减少的初始问题的积分微分自由边界问题，其中正常反射和光滑拟合条件可能会打破，后者然后由连续拟合条件取代。我们表明，在一定的关系模型的参数，最佳停止边界可以唯一地确定为一个二维系统的非线性常微分方程的解决方案的一个组成部分。所得结果可以解释为在跳扩散模型中具有固定和浮动执行价格的永久美式回望期权的定价。
In this paper we present closed form solutions of some discounted optimal stopping problems for the maximum process in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problems to integro-differential free-boundary problems, where the normal-reflection and smooth-fit conditions may break down and the latter then replaced by the continuous-fit condition. We show that, under certain relationships on the parameters of the model, the optimal stopping boundary can be uniquely determined as a component of the solution of a two-dimensional system of nonlinear ordinary differential equations. The obtained results can be interpreted as pricing perpetual American lookback options with fixed and floating strikes in a jump-diffusion model.