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

## TL;DR

This paper investigates the conditions under which the classical Kyle-Back model results hold, showing that certain pricing rules invalidate the folk result and establishing when insider strategies are necessarily absolutely continuous.

## Contribution

It identifies necessary conditions for pricing rules to be consistent with equilibrium and extends the classical Kyle-Back model to a broader setting.

## Key findings

- Certain pricing rules lead to infinite insider value without strategy restrictions.
- Necessary conditions ensure the insider's optimal strategy is absolutely continuous.
- Standard assumptions of absolute continuity are justified under these conditions.

## Abstract

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