Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2023, Vol. 40 ›› Issue (3): 493-502.doi: 10.3969/j.issn.1005-3085.2023.03.012

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Optimal Utility for an Insider

YANG Jianqi   

  1. School of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530003
  • Received:2021-06-16 Accepted:2022-06-01 Online:2023-06-15 Published:2023-08-15
  • Supported by:
    First-class Discipline Construction Project for Statistics in Guangxi (2022SXYB13).

Abstract:

Based on the current jump-diffusion model and logarithmic utility function, the maximum expected utility problem and information utility comparison problem are considered within an insider information market. A measurable random variable with respect to maturity date is used to describe the insider information in the real financial market. On this basis, the insider information market model is constructed, and the general and the insider are defined. The multi-dimensional jump diffusion model is used to describe risky assets. Based on this model, the expected utility maximization problem of investors with two kinds of different information is put forward clearly. By the initial enlargement of filtration, the problems of expected utility maximization of general and insider, respectively, are solved through stochastic methods and explicit utility maximization strategies and corresponding maximization utilities are formulated respectively. Investment strategies are affected by market information. Investors often need to spend certain information costs to obtain information, and different information brings different effects to investors. Under the assumption of the same information cost, rational investors will always choose the information that can bring them more utility. For the purpose of comparing the utilities of different information, information utility ratio is defined as the ratio of two initials for gaining the equivalent maximized expected utility under different information conditions. Then, its five properties and the ratio of general information to insider information are given explicitly.

Key words: insider, expect utility, jump-diffusion model, information utility ratio

CLC Number: