Time evaluation of portfolio for asymmetrically informed traders

TL;DR

This paper analyzes the impact of asymmetric insider information and information delays on optimal portfolio strategies across various financial models using anticipating stochastic calculus.

Contribution

It explicitly computes optimal portfolios for asymmetrically informed traders with delays, comparing performance across multiple classical financial models.

Findings

Privileged information outweighs delay effects in most cases.

Performance depends on the number of delayed information flows and their parameters.

Future information can be valued in terms of time, not just utility.

Abstract

We study the anticipating version of the classical portfolio optimization problem in a financial market with the presence of a trader who possesses privileged information about the future (insider information), but who is also subjected to a delay in the information flow about the market conditions; hence this trader possesses an asymmetric information with respect to the traditional one. We analyze it via the Russo-Vallois forward stochastic integral, i. e. using anticipating stochastic calculus, along with a white noise approach. We explicitly compute the optimal portfolios that maximize the expected logarithmic utility assuming different classical financial models: Black-Scholes-Merton, Heston, Vasicek. Similar results hold for other well-known models, such as the Hull-White and the Cox-Ingersoll-Ross ones. Our comparison between the performance of the traditional trader and the insider, although only asymmetrically informed, reveals that the privileged information overcompensates the delay in all cases, provided only one information flow is delayed. However, when two information flows are delayed, a competition between future information and delay magnitude enters into play, implying that the best performance depends on the parameter values. This, in turn, allows us to value future information in terms of time, and not only utility.