英文标题：
《Transition probability of Brownian motion in the octant and its
application to default modeling》
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作者：
Vadim Kaushansky, Alexander Lipton, Christoph Reisinger
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最新提交年份：
2018
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英文摘要：
We derive a semi-analytic formula for the transition probability of three-dimensional Brownian motion in the positive octant with absorption at the boundaries. Separation of variables in spherical coordinates leads to an eigenvalue problem for the resulting boundary value problem in the two angular components. The main theoretical result is a solution to the original problem expressed as an expansion into special functions and an eigenvalue which has to be chosen to allow a matching of the boundary condition. We discuss and test several computational methods to solve a finite-dimensional approximation to this nonlinear eigenvalue problem. Finally, we apply our results to the computation of default probabilities and credit valuation adjustments in a structural credit model with mutual liabilities.
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中文摘要：
我们推导了在边界有吸收的正八分体中三维布朗运动转移概率的半解析公式。在球坐标系中分离变量会导致在两个角分量中产生的边值问题的特征值问题。主要的理论结果是对原始问题的一个解决方案，表示为对特殊函数和特征值的扩展，必须选择该特征值以允许边界条件的匹配。我们讨论并测试了几种计算方法来解决这个非线性特征值问题的有限维近似。最后，我们将我们的结果应用于具有共同负债的结构性信贷模型中违约概率的计算和信贷估值调整。
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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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