is well defined and is a square integrable martingale, i.e. and f ( . ) is an increasing function. Remark 2.3 Since the final payoff of the stock is given by f ( Z$_{1}$ ) , the above assumption implies that it is always possible to redefine the function f so that In what follows, I will always assume that this equality holds. In this section I address the problem of existence and uniqueness of an equilibrium given by Defini- tion 2.3 in the case of Markovian pricing rule i.e. I consider w ( t ) ≡ 1. Before stating the main result of this section, I need to impose additional conditions on the model to insure that the problem is well-posed. and either or 9 lim t → 1 ∫ t 0 1 | Σ$_{z}$( s ) + σ 2 − s | ds = ∞ (3.3) ∫ 1 0 ( Σ$_{z}$( s ) + σ 2 − s ) − $^{2}$ds < ∞ (3.2) ∫ 0 ( Σ$_{z}$( s ) + σ 2 − s ) − $^{2}$ds < ∞ (3.1) σ 2 = 1 − Σ$_{z}$(1) . (2.7) E [ f $^{2}$( Z$_{1}$ ) ] < ∞ , (2.6) Assumption 2.2 The variance of the firm value, Σ$_{z}$( t ) = ∫ t 0 σ 2 $_{z}$( s ) ds , is finite for any t . Assumption 3.1 For any t ∈ [0 , 1) we have 3 The Markovian Equilibrium