摘要翻译:
本文研究了求解离散时间最优停车问题的仿真优化算法。这类算法在数量金融领域的从业人员中很受欢迎。利用经验过程增量的大偏差理论,我们导出了最优收敛速度,并证明了它们在一般情况下是不可改进的。推导出的速率为优化步骤中所需的仿真路径数的选择提供了指导,这对于任何基于仿真的优化算法的良好性能都是至关重要的。最后,我们给出了一个求解期权定价中最优停止问题的数值例子,说明了我们的理论结果。
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英文标题:
《On the rates of convergence of simulation based optimization algorithms
for optimal stopping problems》
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作者:
Denis Belomestny
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最新提交年份:
2009
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分类信息:
一级分类:Mathematics 数学
二级分类:Optimization and Control 优化与控制
分类描述:Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学,线性规划,控制论,系统论,最优控制,博弈论
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一级分类:Mathematics 数学
二级分类:Probability 概率
分类描述:Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用:例如中心极限定理,大偏差,随机微分方程,统计力学模型,排队论
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一级分类:Quantitative Finance 数量金融学
二级分类:Computational Finance 计算金融学
分类描述:Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法,包括蒙特卡罗,偏微分方程,格子和其他数值方法,并应用于金融建模
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英文摘要:
In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large deviation theory for the increments of empirical processes, we derive optimal convergence rates and show that they can not be improved in general. The rates derived provide a guide to the choice of the number of simulated paths needed in optimization step, which is crucial for the good performance of any simulation based optimization algorithm. Finally, we present a numerical example of solving optimal stopping problem arising in option pricing that illustrates our theoretical findings.
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PDF链接:
https://arxiv.org/pdf/0909.3570