论文标题
局部随机波动率模型中的非常规McKean- vlasov方程和校准问题
Non--regular McKean--Vlasov equations and calibration problem in local stochastic volatility models
论文作者
论文摘要
为了解决金融中校准局部随机波动率模型存在的问题，我们研究了一类McKean-vlasov方程，其中最小的连续性假设对系数施加了最小的连续性假设。也就是说，漂移系数，尤其是挥发性系数不一定在沃斯尔斯坦拓扑的度量变量中连续。在本文中，我们提供了一个存在结果，并显示了$ n $的近似值 - 粒子系统或这种类型的McKean-vlasov方程的混乱传播。作为直接结果，我们能够推断出校准的局部随机波动率模型的存在，以选择随机波动率参数。还证明了混乱结果的相关传播。
In order to deal with the question of the existence of a calibrated local stochastic volatility model in finance, we investigate a class of McKean--Vlasov equations where a minimal continuity assumption is imposed on the coefficients. Namely, the drift coefficient and, in particular, the volatility coefficient are not necessarily continuous in the measure variable for the Wasserstein topology. In this paper, we provide an existence result and show an approximation by $N$--particle system or propagation of chaos for this type of McKean--Vlasov equations. As a direct result, we are able to deduce the existence of a calibrated local stochastic volatility model for an appropriate choice of stochastic volatility parameters. The associated propagation of chaos result is also proved.
