since θ is inconspicuous, Y$_{1}$ ∼ N (0 , 1). Since Z$_{1}$ ∼ N (0 , 1) by definition, one can have f ( Z$_{1}$ ) = h ( Y$_{1}$ ) if and only if f = h almost everywhere, hence H ∗ is indeed a unique inconspicuous pricing rule. ■ In this section I address the problem of existence of an equilibrium given by Definition 2.3 in the more general case of non Markovian pricing rule, i.e. I consider general weighting functions w ( t ) satisfying Definition 2.2 thus allowing the market maker to assign different weights to the information she receives. As in the case of Markovian pricing rule, the existence of an equilibrium result is driven by the existence of a finite upper bound on the informed agent’s value function, and the characterization of the trading strategies which attain it. This characterization is summarized in the following proposition. Proposition 4.1 Suppose that Assumptions 2.1 and 2.2 are satisfied. Then, given an admissible pricing rule w ( t ) defined by (2.4) with σ i y < σ i +1 y for any i and ( H, w ) ∈ H with H satisfying the partial differential equation an admissible trading strategy θ ∗ ∈ A ( H, w ) is optimal for insider if and only if: Therefore, as in the case of Markovian pricing rule, the optimal strategy of the insider does not alter quadratic variation of total order process, does not add jumps to it and is uncorrelated with it. But, differently from the Markovian case, it follows from (4.2) that in this setting it is optimal for 20 2. The weighted total order, ξ ∗ t = ∫ t 0 w ( s ) dθ ∗ s − + ∫ t 0 w ( s ) dB 2 s satisfies 1. The process θ ∗ t is continuous and has bounded variation. h$_{i}$ ( ξ ∗ t$_{i}$ ) = H ( ξ ∗ $_{t$_{i}$}$, t$_{i}$ ) = F ( Z$_{t}$$_{i}$, t$_{i}$ ) . (4.2) H$_{t}$ ( y, t ) + w $^{2}$( t ) 2 H$_{yy}$ ( y, t ) = 0 (4.1) 4 Non Markovian equilibrium