摘要翻译：
我们考虑了平方Bessel过程的精确路径采样，以及其他一些连续时间Markov过程，如CIR模型、常方差弹性扩散模型和超几何扩散，它们都可以通过变量的变化、时间和尺度的变换和/或测度的变化从平方Bessel过程中得到。所有这些扩散在数学金融学中被广泛用于资产价格、市场指数和利率的建模。我们给出了平方贝塞尔桥和平方贝塞尔过程在零吸收或无吸收情况下的概率分布如何归结为随机gamma分布。此外，为了吸收随机过程，我们提出了一种新的桥式采样技术，该技术基于零初击时间条件。这种方法使我们可以简化模拟方案。以路径相关期权的定价为例说明了新的方法。
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英文标题：
《Exact Simulation of Bessel Diffusions》
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作者：
Roman N. Makarov and Devin Glew
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最新提交年份：
2009
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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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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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英文摘要：
  We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be obtained from a squared Bessel process by using a change of variable, time and scale transformation, and/or change of measure. All these diffusions are broadly used in mathematical finance for modelling asset prices, market indices, and interest rates. We show how the probability distributions of a squared Bessel bridge and a squared Bessel process with or without absorption at zero are reduced to randomized gamma distributions. Moreover, for absorbing stochastic processes, we develop a new bridge sampling technique based on conditioning on the first hitting time at zero. Such an approach allows us to simplify simulation schemes. New methods are illustrated with pricing path-dependent options.
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PDF链接：
https://arxiv.org/pdf/0910.4177