Risk-sharing and probabilistic network structure

This paper studies the impact of a probabilistic risk-sharing network structure on the optimal portfolio composition. We show that, even assuming identical agents, we are able to differentiate their optimal risk-choice once we assume the link-structure defining their relationship probabilistic. In particular, the final agent's portfolio composition is function of his location in the network. If we assume positive asset-correlation coefficients, the relative location of a player in the graph influences his risk-behaviour as much as those of his direct and indirect partners in a not-straightforward way. We analyse also two potential "centrality measures" able to select the key-player in the risk-sharing network. The findings may help to select the "central" agent in a risk-sharing community and to forecast the risk-exposure of the players. Finally, this paper may explain natural differences between identical rational agents' choices emerging in a probabilistic network setup.