content_image/310068.jpg content_image/310067.jpg content_image/310066.jpg content_image/310065.jpg content_image/310064.jpg
is well defined and is a square integrable martingale, i.e. 

and f ( . ) is an increasing function. 

<img src='content_image/310068.jpg'>

Assumption 2.2 The variance of the firm value, Σ$_{z}$( t ) = ∫ t 0 σ 2 $_{z}$( s ) ds , is finite for any t . 

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. 

## 3 The Markovian Equilibrium 

<img src='content_image/310067.jpg'>

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. 

Assumption 3.1 For any t ∈ [0 , 1) we have 

and either 

or 

<img src='content_image/310066.jpg'>

<img src='content_image/310065.jpg'>

<img src='content_image/310064.jpg'>

