Optimal Investment with Insider Information Using Skorokhod & Russo-Vallois Integration

Mauricio Elizalde (), Carlos Escudero () and Tomoyuki Ichiba ()
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Mauricio Elizalde: Departamento de Matemáticas Fundamentales Universidad Nacional de Educación a Distancia Calle de Juan del Rosal, 10
Carlos Escudero: Departamento de Matemáticas Fundamentales Universidad Nacional de Educación a Distancia Calle de Juan del Rosal, 10
Tomoyuki Ichiba: University of California Santa Barbara

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 3, No 8, 43 pages

Abstract: Abstract We study the maximization of the logarithmic utility for an insider with different anticipating techniques. Our aim is to compare the utilization of Russo-Vallois forward integral and Skorokhod integral in this context. Theoretical analysis and illustrative numerical examples showcase that the Skorokhod insider outperforms the forward insider. This remarkable observation stands in contrast to the scenario involving risk-neutral traders. Furthermore, an ordinary trader could surpass both insiders if a significant negative fluctuation in the driving stochastic process leads to a sufficiently negative final value. These findings underline the intricate interplay between anticipating stochastic calculus and nonlinear utilities, which may yield non-intuitive results from the financial viewpoint.

Keywords: Insider trading; Anticipating calculus; Portfolio optimization; Russo-Vallois forward integral; Skorokhod integral; Malliavin derivative; Anticipative Girsanov transformations; 60H05; 60H07; 60H10; 60H30; 91G10 (search for similar items in EconPapers)
JEL-codes: C02 C61 G11 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02789-z

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