# How to model the different returns of agents with different information information

For a seminar, I would like to graphically represent the returns made by agents of different information standpoints. In other words, say I have a market tuple $$(\Omega, \mathbb{F}, P,S)$$ where $$S$$ is a stochastic process representing the price process of the one risky asset. Next say we have $$k$$ agents who respectively have information represented by the filtration $$\mathbb F_{i}$$ for the $$i$$-th agent $$(i = 1,...,k)$$. Now, let $$\mathbb F \subseteq \mathbb F_{1} \subseteq ...\subseteq \mathbb F_{k}$$.

How can I model the "random walks" of the different agents and further how can I define the $$\sigma-$$algebras or filtrations in a programming sense in order to make sense and compute them?

Grateful for any advice.

• Oh boy, this is a very tough problem to model, perhaps unsolvable without major conceptual breakthroughs in Financial Economics and Game Theory. Good luck. – noob2 Mar 6 at 14:19
• @noob2 any other ideas to get some insightful simulations/graphics of insider information? – user9078057 Mar 6 at 23:57
• I would google for "extensions to multivariate kyle model" and see if anything comes up. That sounds like more than one Ph.D thesis !!!!! – mark leeds Mar 7 at 14:24