Remark 2.2 Due to condition 4 on the admissible pricing rules, the insider can infer the total order process from the price process by inverting H ( ∫ t 0 w ( s ) dY$_{s}$, t ) = P$_{t}$ . Therefore, since I will be considering rational expectations equilibria, and because w ( s ) is strictly positive, she can infer the total order process Y$_{t}$ and, since she knows her own total order process θ$_{t}$ , she can deduce B 2 t = Y$_{t}$ − θ$_{t}$ from it. As a consequence, the filtration of the insider can be written as F I t = F B $^{2}$,Z t = F B $^{2}$,B1 t ∨ σ ( v ) , where σ ( v ) is the sigma algebra generated by the random variable v . Given these definitions of admissible pricing rules and trading strategies, it is now possible to formally define the market equilibrium as follows. Definition 2.3 A pair (( H $^{∗}$, w$^{∗}$) , θ $^{∗}$) is an equilibrium if ( H $^{∗}$, w$^{∗}$) is an admissible pricing rule, θ ∗ is admissible strategy, and: Moreover, a pricing rule ( H $^{∗}$( y, t ) , w $^{∗}$( t )) is an inconspicuous equilibrium pricing rule if there exists an inconspicuous insider trading strategy θ ∗ such that (( H $^{∗}$, w$^{∗}$) , θ $^{∗}$) is an equilibrium. Additionally, to define a well behaved problem I impose the following technical conditions on the model parameters. 8 Assumption 2.1 The fundamental value of the risky stock, F ( z, t ) , given by 1. Given θ $^{∗}$, ( H $^{∗}$, w$^{∗}$) is a rational pricing rule, i.e. it satisfies 2. Given ( H $^{∗}$, w$^{∗}$) , θ ∗ solves the optimization problem F ( Z$_{t}$, t ) = E [ f ( Z$_{1}$ ) |F Z t ] (2.5) sup$_{θ}$$_{∈A}$$_{(}$$_{H}$ $^{∗}$,w∗ $_{)}$E [ ( f ( Z$_{1}$ ) − P$_{1}$ ) θ$_{1}$ + ∫ 1 0 θ$_{s}$$_{−}$dP$_{s}$ ] H (∫ t 0 w ( s ) dY$_{s}$, t ) = E [ f ( Z$_{1}$ ) |F M t ] .