论文标题
在贝塞尔电位空间中的局部局部差异方程的解决方案中，具有期权定价模型的应用
On solutions of a partial integro-differential equation in Bessel potential spaces with applications in option pricing models
论文作者
论文摘要
在本文中，我们着重于非局部非线性部分局部差异方程（PIDE）的定性特性。使用抽象半连续抛物线方程的理论，我们证明了贝塞尔电位空间规模的解决方案的存在和独特性。我们的目的是概括已知的存在结果，以采取一系列lévy措施，包括强大的奇异核。 作为一个应用程序，我们考虑在金融数学中产生的一类辅助。经典的线性黑色 - choles模型依赖于几个限制性假设，例如流动性和市场的完整性。放松整个市场假设，并假设为基础股票价格过程征收随机过程动态，我们通过派德获得了定价选项的模型。我们研究了一个定价呼叫的模型，并在带有跳跃的征费随机过程后对基本资产进行了选择。我们证明了解决方案的存在和独特性，代表了在征收随机过程下定价美国选择风格的线性互补问题的近似。我们还提出了数值结果和对基础资产动态基础的各种征费随机过程的期权价格的比较。
In this paper we focus on qualitative properties of solutions to a nonlocal nonlinear partial integro-differential equation (PIDE). Using the theory of abstract semilinear parabolic equations we prove existence and uniqueness of a solution in the scale of Bessel potential spaces. Our aim is to generalize known existence results for a wide class of Lévy measures including with a strong singular kernel. As an application we consider a class of PIDEs arising in the financial mathematics. The classical linear Black-Scholes model relies on several restrictive assumptions such as liquidity and completeness of the market. Relaxing the complete market hypothesis and assuming a Levy stochastic process dynamics for the underlying stock price process we obtain a model for pricing options by means of a PIDE. We investigate a model for pricing call and put options on underlying assets following a Levy stochastic process with jumps. We prove existence and uniqueness of solutions to the penalized PIDE representing approximation of the linear complementarity problem arising in pricing American style of options under Levy stochastic processes. We also present numerical results and comparison of option prices for various Levy stochastic processes modelling underlying asset dynamics.
