coming from the trading activity. Note that setting σ$_{z}$ ≡ 0, the resulting market would be the static information one considered by [2]. Note also that the above market structure implies that the insider’s optimal trading strategy takes into account the feedback effect i.e. the that prices react to her trading strategy according to equation (2.1). Identifying the optimal insider’s strategy is equivalent to the problem of finding the rational expectations equilibrium of this market, i.e. a pair consisting of an admissible price functional and an admissible trading strategy such that: a) given the price functional the trad- ing strategy is optimal, and b) given the trading strategy the price functional satisfies (2.1). To formalize this definition, we first need to define the sets of admissible pricing rules and trading strategies. Although it is standard in the insider trading literature to limit the set of admissible strategies to absolutely continuous ones, in what follows I consider a much broader class of strategies given by the set of semimartingales satisfying some standard technical conditions that eliminate doubling strategies. The formal definition of the set of admissible trading strategies is summarized in the following definition. Definition 2.1 An insider’s trading strategy, θ$_{t}$ , is admissible for a given pricing rule ( H ( y, t ) , w ( t )) ( θ ∈ A ( H, w ) ) if θ$_{t}$ is F I t adapted semimartingale, and no doubling strategies are allowed i.e. Moreover, we call the insider’s trading strategy inconspicuous if Y$_{t}$ = θ$_{t}$ + B 2 t is a Brownian motion on its own filtration F Y t (since in this case the presence of the insider is undetectable). Remark 2.1 An equilibrium in which the optimal insider’s trading strategy is inconspicuous is a desirable feature of any insider trading model, and I will show that in this setting such an equilibrium exists. In fact, given the potentially high cost associated with being identified as an insider, it might be reasonable to consider only this type of equilibrium. E [∫ 1 0 H 2 (∫ t 0 w ( s ) dθ$_{s}$$_{−}$ + ∫ t 0 w ( s ) dB 2 $_{s}$, t ) dt ] < ∞ . (2.3) 6