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莱维期权定价偏积分微分方程的解存在唯一性

文章 arXiv papers · 作者: Daniel Sevcovic et al.
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总结

论文研究用于含跳跃金融模型的多维非局部偏积分微分方程（PIDEs）。论文应用抽象半线性抛物方程理论，在贝塞尔势空间中证明解的存在性和唯一性，将此前的一维结果扩展到多维。分析涵盖一大类在零点附近和无穷远处满足增长条件的莱维测度。

在期权定价方面，论文考察标的资产遵循带跳跃莱维过程的布莱克—斯科尔斯模型。论文还研究一种一维非线性定价应用，其中位移函数可以取决于预先指定的大型投资者的股票交易策略。这些结果确立了该数学框架的适定性；文档没有给出数值定价比较或实证交易证据，所述应用也仅限于文中描述的模型设定。

核心观点

  • 分析将PIDE的存在性和唯一性结果从一维空间扩展到多维空间。
  • 研究在一系列贝塞尔势空间中考察解。
  • 该框架适用于在原点附近和无穷远处满足指定增长条件的莱维测度。
  • 期权定价应用采用由跳跃驱动的莱维过程，还包括与大型投资者交易策略相关的非线性设定。

标签

期权衍生品定价统计学
全文
# 2106.10498


# Multidimensional linear and nonlinear partial integro-differential equation in Bessel potential spaces with applications in option pricing









The purpose of this paper is to analyze solutions of a non-local nonlinear partial integro-differential equation (PIDE) in multidimensional spaces. Such class of PIDE often arises in financial modeling. We employ the theory of abstract semilinear parabolic equations in order to prove existence and uniqueness of solutions in the scale of Bessel potential spaces. We consider a wide class of Lévy measures satisfying suitable growth conditions near the origin and infinity. The novelty of the paper is the generalization of already known results in the one space dimension to the multidimensional case. We consider Black-Scholes models for option pricing on underlying assets following a Lévy stochastic process with jumps. As an application to option pricing in the one-dimensional space, we consider a general shift function arising from nonlinear option pricing models taking into account a large trader stock-trading strategy. We prove existence and uniqueness of a solution to the nonlinear PIDE in which the shift function may depend on a prescribed large investor stock-trading strategy function.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。