DYNAMIC UTILITY AND RELATED NONLINEAR SPDES DRIVEN BY LÉVY NOISE

IF 0.5 Q4 BUSINESS, FINANCE

International Journal of Theoretical and Applied Finance Pub Date : 2022-02-28 DOI:10.1142/s0219024922500042

ANIS MATOUSSI, MOHAMED MRAD

引用次数: 3

Abstract

In this work, we study a class of consistent dynamic utilities in a incomplete financial market including jumps. First, we show that the dynamic utility is solution of a non-linear second-order stochastic partial integro-differential equation (SPIDE). Second, a complete study of the primal and the dual problems, allows us, firstly, to establish a connection between the utility-SPIDE and two SDEs satisfied by the optimal processes. Based on this connection, stochastic flow technics for SDEs and characteristic method, the SPIDE is completely solved and monotony and concavity properties of the solution are proved.

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由lÉvy噪声驱动的动态效用和相关非线性速度

本文研究了不完全金融市场中包含跳跃的一类一致动态效用。首先，我们证明了动态效用是非线性二阶随机偏积分微分方程(SPIDE)的解。其次，对原始问题和对偶问题的完整研究，使我们能够首先建立效用- spide与最优过程满足的两个SDEs之间的联系。在此基础上，结合SDEs的随机流动技术和特征法，对SPIDE进行了完全求解，并证明了解的单调性和凹凸性。

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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来源期刊

International Journal of Theoretical and Applied Finance BUSINESS, FINANCE-

CiteScore

1.10

自引率

20.00%

发文量

期刊介绍： The shift of the financial market towards the general use of advanced mathematical methods has led to the introduction of state-of-the-art quantitative tools into the world of finance. The International Journal of Theoretical and Applied Finance (IJTAF) brings together international experts involved in the mathematical modelling of financial instruments as well as the application of these models to global financial markets. The development of complex financial products has led to new challenges to the regulatory bodies. Financial instruments that have been designed to serve the needs of the mature capitals market need to be adapted for application in the emerging markets.