摘要翻译：
本文主要研究可转换债券的投资者和发行人行为的最优行权策略。这意味着股票价格建模、收益计算和最小最大优化问题的解决。股票价格（标的资产）是在其价值的几何布朗运动假设下建模的。采用蒙特卡罗方法计算实际收益，并以此为目标函数。用无导数下山单纯形法求解最小最大优化问题。所进行的数值实验为下山单纯形法中初始单纯形的适当大小、基础资产生成轨迹的数目、问题的大小以及投资者和发行人行为的初始轨迹的选择提供了建议。
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英文标题：
《Adapted Downhill Simplex Method for Pricing Convertible Bonds》
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作者：
Kateryna Mishchenko, Volodymyr Mishchenko and Anatoliy Malyarenko
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最新提交年份：
2007
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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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英文摘要：
  The paper is devoted to modeling optimal exercise strategies of the behavior of investors and issuers working with convertible bonds. This implies solution of the problems of stock price modeling, payoff computation and min-max optimization.   Stock prices (underlying asset) were modeled under the assumption of the geometric Brownian motion of their values. The Monte Carlo method was used for calculating the real payoff which is the objective function. The min-max optimization problem was solved using the derivative-free Downhill Simplex method.   The performed numerical experiments allowed to formulate recommendations for the choice of appropriate size of the initial simplex in the Downhill Simplex Method, the number of generated trajectories of underlying asset, the size of the problem and initial trajectories of the behavior of investors and issuers.
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PDF链接：
https://arxiv.org/pdf/0710.0241