考虑交易成本的随机波动模型下的美式期权估值

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-04-10 DOI:10.1080/17442508.2014.989525

Andrea Cosso, D. Marazzina, C. Sgarra

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引用次数: 2

摘要

本文分析了考虑交易成本的随机波动率模型下的美式期权估值问题。我们将证明它可以被表述为一个奇异随机最优控制问题，证明了相关Hamilton-Jacobi-Bellman偏微分方程黏度解的存在唯一性。此外，在通过选择合适的效用函数进行降维之后，我们将提供一个数值示例，说明如何在当前的建模框架中计算美国期权价格。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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American option valuation in a stochastic volatility model with transaction costs

In the present paper we analyse the American option valuation problem in a stochastic volatility model when transaction costs are taken into account. We shall show that it can be formulated as a singular stochastic optimal control problem, proving the existence and uniqueness of the viscosity solution for the associated Hamilton–Jacobi–Bellman partial differential equation. Moreover, after performing a dimensionality reduction through a suitable choice of the utility function, we shall provide a numerical example illustrating how American options prices can be computed in the present modelling framework.

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.