英文标题：
《Explicit solutions of quadratic FBSDEs arising from quadratic term
structure models》
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作者：
Cody Hyndman and Xinghua Zhou
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最新提交年份：
2014
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英文摘要：
We provide explicit solutions of certain forward-backward stochastic differential equations (FBSDEs) with quadratic growth. These particular FBSDEs are associated with quadratic term structure models of interest rates and characterize the zero-coupon bond price. The results of this paper are naturally related to similar results on affine term structure models of Hyndman (Math. Financ. Econ. 2(2):107-128, 2009) due to the relationship between quadratic functionals of Gaussian processes and linear functionals of affine processes. Similar to the affine case a sufficient condition for the explicit solutions to hold is the solvability in a fixed interval of Riccati-type ordinary differential equations. However, in contrast to the affine case, these Riccati equations are easily associated with those occurring in linear-quadratic control problems. We also consider quadratic models for a risky asset price and characterize the futures price and forward price of the asset in terms of similar FBSDEs. An example is considered, using an approach based on stochastic flows that is related to the FBSDE approach, to further emphasize the parallels between the affine and quadratic models. An appendix discusses solvability and explicit solutions of the Riccati equations.
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中文摘要：
我们给出了某些具有二次增长的正倒向随机微分方程（FBSDE）的显式解。这些特殊的FBSDE与利率的二次期限结构模型相关联，并表征零息票债券价格。由于高斯过程的二次泛函和仿射过程的线性泛函之间的关系，本文的结果自然与Hyndman（Math.Financ.Econ.2（2）：107-1282009）的仿射项结构模型的类似结果相关。与仿射情形类似，Riccati型常微分方程显式解成立的一个充分条件是在固定区间内可解。然而，与仿射情况相比，这些Riccati方程很容易与线性二次控制问题中的方程相关联。我们还考虑了风险资产价格的二次模型，并根据类似的FBSDE描述了资产的期货价格和远期价格。考虑一个例子，使用与FBSDE方法相关的基于随机流的方法，进一步强调仿射模型和二次模型之间的相似性。附录讨论了Riccati方程的可解性和显式解。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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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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