勷勤数学•专家报告

题      目：Deep Operator Network Expressivity for European Option Pricing under Exponential Levy Models

报  告  人：张功球 副教授  (邀请人：杨舟)

                                         香港中文大学（深圳）

时      间： 9月26日  09：30-10:30

地     点：数科院西楼二楼会议室

报告人简介:

        张功球，香港中文大学（深圳）助理教授、博士生导师、深圳市大数据研究院研究科学家。主要研究金融数学、金融科技、计算金融等方向。研究成果发表于 Operations Research, Mathematical Finance, Finance and Stochastics, Journal of Economic Dynamics and Control, SIAM Journal on Financial Mathematics, SIAM Journal on Scientific Computing等期刊，主持多项国家自然科学基金与深圳市科创委项目。

摘      要：

        In this paper, we obtain the expression rates of the deep operator network (DeepONet) for learning the pricing operator that maps from the space of coefficient functions to that of pricing functions for European options under exponential time-inhomogeneous L´evy models. Under some structural assumptions on the payoff function, we show that DeepONet overcomes the curse of dimensionality for this problem, i.e., it can achieve an arbitrary uniform error of ε > 0 with the network size growing polynomially in the number of underlying assets (d) and 1/ε. With another set of assumptions on the payoff, we show that the error of DeepONet can decay exponentially in its size, albeit with the implied constant possibly growing exponentially in d. This work is joint with Lingfei Li, Yeda Cui and Wenyong Zhang.

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