Abstract 
: 
Real options present a wide topic in investment litterature nowadays. However, despite big
advances in the single asset investment pricing, the theory is miser of informations about
problems involving more than one asset. We show in this paper that using dynamic programming,
one can ﬁnd an analytic trigger for a three assets simple exchange problem. Although we get a
forward investment rule, one can not ﬁnd the precise option value ex ante but only an average
value. The precise option value depends on the ﬁrst exit time from the continuation region which
is stochastic.
This is a quite intuitive effect of the course of dimensionality of the problem. Valuating a
single asset project gives a single condition for the optimal decision rule. The same holds for the
simple exchange problem with two assets since the value of the project just depends on the price
over cost ratio. In a three assets problem, as the project don’t depend anymore of a single state
variable, one can’t region.
