On pricing rules and optimal strategies in general Kyle-Back models

Speaker: 

Albina Danilova, Visiting Associate Professor, Questrom School of Business, Boston University

Description: 

The folk result in Kyle-Back models states that the value function of the insider remains unchanged when her admissible strategies are restricted to absolutely continuous ones.  In this talk I will show that,  for a large class of pricing rules used in current literature, the value function of the insider can be finite when her strategies are restricted to be absolutely continuous and infinite when this restriction is not imposed. This implies that the folk result doesn't hold for  those pricing rules and that they are not consistent with equilibrium.  I will derive the necessary conditions for a pricing rule to be consistent with equilibrium and prove that, when a pricing rule satisfies these necessary conditions, the insider's optimal strategy is absolutely continuous, thus obtaining the classical result in a more general setting.  

This, furthermore, allows to justify the standard assumption of absolute continuity of insider's strategies since one can construct a pricing rule satisfying the derived necessary conditions that yield the same price process as the pricing rules employed in the modern literature when insider's strategies are absolutely continuous.

Event Topic

Mathematical Finance, Stochastic Analysis, and Machine Learning