The insider trading problem in a jump-binomial model. (English) Zbl 1536.91316
This extensive study investigates insider trading in a jump-binomial financial model, exploring the advantages of insider information and devising hedging strategies. It relies on Blanchet-Scalliet and Jeanblanc’s filtration enlargement results [C. Blanchet-Scalliet and M. Jeanblanc, in: From probability to finance. Lecture notes of BICMR summer school on financial mathematics, Beijing International Center for Mathematical Research, Beijing, China, May 29 – June 9, 2017. Singapore: Springer. 71–144 (2020; Zbl 1453.60097)] and Halconruy’s stochastic analysis [H. Halconruy, Electron. J. Probab. 27, Paper No. 164, 39 p. (2022; Zbl 1511.60079)]. It extends and parallels prior findings in discrete-time and incomplete markets.
In the model under consideration, there are two investors: a regular agent and an insider. Both are presumed to have negligible influence on market prices, although the insider possesses private, strategic information from the outset. The findings are presented from two aspects: firstly, from the standpoint of information theory, examining the advantage the extra knowledge affords the insider, and secondly, considering the insider’s role as a separate investor.
Initially, the author introduces tools such as the jump-binomial model, stochastic analysis techniques, and filtration enlargement results. Next an examination of the advantages of additional information, computing expected utilities for both agent and insider and linking them to information theory. The maximum expected utility for both the regular agent and the insider is calculated and contrasted; aiming to quantify the insider’s advantage and assess the benefit derived from the extra information available. Based on optimisation arguments, the aim is to assess the advantage obtained by the insider through utilizing supplementary information, with novel explicit formulas for the expected extra utility (logarithmic, exponential, power) in contrast to a standard agent being derived. An added feature is to structure an optimal hedging strategy for the insider.
In the model under consideration, there are two investors: a regular agent and an insider. Both are presumed to have negligible influence on market prices, although the insider possesses private, strategic information from the outset. The findings are presented from two aspects: firstly, from the standpoint of information theory, examining the advantage the extra knowledge affords the insider, and secondly, considering the insider’s role as a separate investor.
Initially, the author introduces tools such as the jump-binomial model, stochastic analysis techniques, and filtration enlargement results. Next an examination of the advantages of additional information, computing expected utilities for both agent and insider and linking them to information theory. The maximum expected utility for both the regular agent and the insider is calculated and contrasted; aiming to quantify the insider’s advantage and assess the benefit derived from the extra information available. Based on optimisation arguments, the aim is to assess the advantage obtained by the insider through utilizing supplementary information, with novel explicit formulas for the expected extra utility (logarithmic, exponential, power) in contrast to a standard agent being derived. An added feature is to structure an optimal hedging strategy for the insider.
Reviewer: John O’Hara (Colchester)
Keywords:
insider trading; trinomial model; enlargement of filtrations; Malliavin’s calculus; utility maximizationReferences:
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