We model the formation of cross-holding network structures. Each agent can
invest in an individual primitive asset or hold shares of others whose value is conditional
on their respective investment decisions. When an agent holds shares of
many distinct and independent players, she is able to diversify her asset portfolio
risk. However, in a chain of cross-exposures, she could indirectly find herself
exposed to third agents whose expected payoff is perceived as uncertain in the
sense of Knightian-uncertainty. As a direct consequence of this, the optimal holdings
and cross-exposure level of each agent will be in part conditional on her risk
and ambiguity aversion attitude. We characterize the optimal and the stable network structures which arise in this environment; respectively, these are the structures which maximize a utilitarian welfare function and the ones which emerge
endogenously. Sparse networks are optimal and stable when the cost per-link is
high and the players are more sensitive to diversification than uncertainty, while
the opposite is true for dense networks. In general, we find that the architecture of
the stable networks is similar to the optimal ones but not necessarily of the same
density; individual agents fail to internalize the positive/negative externality due
to the activation of a link toward another peer. The model proposes a new alternative interpretation for some of the structural changes observed in financial
markets pre and post-crisis.