摘要翻译：
本文论证了诚实时代概念对金融建模的有用性和重要性。它研究的是一个资产价格跟随跳扩散的金融市场。市场模型的核心组成部分是其增长最优投资组合(GOP)，它使严格正投资组合的增长率最大化。当以GOP为单位表示时，主要安全账户价格是非负的局部鞅。在所提出的框架中，不需要存在等价的风险中性概率测度。以GOP为标量，以现实世界概率为定价度量，衍生品价格是对相应未来收益的条件期望。当一个没有正跳跃的投资组合的全局最大值达到时，以GOP为单位表示，这是一个诚实时间的一般表示。我们给出了这种诚实时间定律的一般公式，并在此框架下计算了投资组合全局最大值的条件分布。此外，我们给出了终值为投资组合全局极大值函数的一致可积鞅的随机积分表示。这些公式具有模型无关性和通用性。我们还将我们的结果专门用于一些例子，在这些例子中，我们对冲了在诚实的时间到达的回报。
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英文标题：
《On honest times in financial modeling》
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作者：
Ashkan Nikeghbali and Eckhard Platen
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最新提交年份：
2008
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分类信息：

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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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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英文摘要：
  This paper demonstrates the usefulness and importance of the concept of honest times to financial modeling. It studies a financial market with asset prices that follow jump-diffusions with negative jumps. The central building block of the market model is its growth optimal portfolio (GOP), which maximizes the growth rate of strictly positive portfolios. Primary security account prices, when expressed in units of the GOP, turn out to be nonnegative local martingales. In the proposed framework an equivalent risk neutral probability measure need not exist. Derivative prices are obtained as conditional expectations of corresponding future payoffs, with the GOP as numeraire and the real world probability as pricing measure. The time when the global maximum of a portfolio with no positive jumps, when expressed in units of the GOP, is reached, is shown to be a generic representation of an honest time. We provide a general formula for the law of such honest times and compute the conditional distributions of the global maximum of a portfolio in this framework. Moreover, we provide a stochastic integral representation for uniformly integrable martingales whose terminal values are functions of the global maximum of a portfolio. These formulae are model independent and universal. We also specialize our results to some examples where we hedge a payoff that arrives at an honest time.
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PDF链接：
https://arxiv.org/pdf/0808.2892