论文标题
具有非线性黑色 - choles-type方程的对手风险模型中的单调方法
Monotone methods in counterparty risk models with non-linear Black-Scholes-type equations
论文作者
论文摘要
在交易对手风险模型中研究了非线性黑色 - 甲型型方程。非线性反应函数的均匀Lipschitz-continusion上的经典假设允许将半线性黑色 - 甲梁方程等效地转换为具有单调非线性反应函数和不均匀的线性扩散方程的标准抛物线问题。这种设置使我们能够构建单调，增加或减少的方案，该方案单调地收敛到真实解决方案。由于该问题的任何数值解决方案通常使用大多数计算能力来计算非均匀线性扩散方程的近似解，因此我们也讨论了这个问题，并提出了几种解决方案方法，包括基于蒙特卡洛和有限差异/元素的解决方案方法。
A non-linear Black-Scholes-type equation is studied within counterparty risk models. The classical hypothesis on the uniform Lipschitz-continuity of the non-linear reaction function allows for an equivalent transformation of the semi-linear Black-Scholes equation into a standard parabolic problem with a monotone non-linear reaction function and an inhomogeneous linear diffusion equation. This setting allows us to construct a scheme of monotone, increasing or decreasing, iterations that converge monotonically to the true solution. As typically any numerical solution of this problem uses most computational power for computing an approximate solution to the inhomogeneous linear diffusion equation, we discuss also this question and suggest several solution methods, including those based on Monte Carlo and finite differences/elements.
