for every history st .
A portfolio θi for every agent i is a vector (θst)st∈St,t∈N+ of shares held
of the J trees in every history st, where θst = (θjst )j is the vector of holdings
in history st and θjst is the holding of j in this same history st . Every agent
i has an initial portfolio θi0 at date 0.
Every agent i does not have any information about P , the true probability
measure from nature draws the states; however agent i has a subjective
belief about nature represented by a probability measure Pi on (S∞, Γ). We
assume that dPti (s) > 0 for every infinite history s and every period t, to
avoid problems of existence as pointed in Araujo and Sandroni (1999).
Every agent derives some utility in any history from consuming the only
consumption good present in the economy. We assume that agent i ranks
all the possible future consumption sequences c = (cst )st∈St,t∈N+ according to
the utility function
Ui(c) = EPi X (βi)tui(ct) , (1)
t∈N+
where βi ∈ (0, 1) is the intertemporal discount factor, ui is a strictly increas-
ing, strictly concave and continuously differentiable function. We assume
that ui satisfies the Inada condition, namely (ui)0(c) 7→ ∞ as c 7→ 0.
The budget constraint faced in every history st by agent i is
cst+Xqsjθjs ≤ wsi +Xdjs θjs +Xqsjθjs (2)
t st st st st st-1 st st-1
j jj
cst ≥ 0, (3)