最优多重停点的解析递推法：离散化和位相型拟合
An analytic recursive method for optimal multiple stopping: Canadization and phase-type fitting
摘要：
研究了由谱负Levy过程驱动的呼叫型支付的最优多重停止问题。停时由常数折射时间分隔，并且贴现率可以是正的或负的。该计算涉及的分布的利维过程在一个恒定的地平线，因此解决方案一般不能得到解析。受Carr（1998）成熟度随机化技术的启发，我们用独立同分布的Erlang随机变量来近似折射时间。此外，拟合随机跳相型分布，我们的方法涉及到重复积分的预解测度写在底层Levy过程的尺度函数。我们推导出一个递归算法来计算封闭形式的价值函数，并依次确定最佳的行使阈值。一系列的数值例子提供比较我们的解析公式从蒙特卡罗模拟的结果。
英文摘要：
We study an optimal multiple stopping problem for call-type payoff driven by a spectrally negative Levy process. The stopping times are separated by constant refraction times, and the discount rate can be positive or negative. The computation involves a distribution of the Levy process at a constant horizon and hence the solutions in general cannot be attained analytically. Motivated by the maturity randomization (Canadization) technique by Carr (1998), we approximate the refraction times by independent, identically distributed Erlang random variables. In addition, fitting random jumps to phase-type distributions, our method involves repeated integrations with respect to the resolvent measure written in terms of the scale function of the underlying Levy process. We derive a recursive algorithm to compute the value function in closed form, and sequentially determine the optimal exercise thresholds. A series of numerical examples are provided to compare our analytic formula to results from Monte Carlo simulation.
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