A network approach to risk theory and portfolio selection

In the context of portfolio theory, the evaluation of risk is of paramount relevance. In this respect, the connections among the risky assets of the portfolio should be carefully explored. This paper elaborates on this topic. We define a portfolio through a network, whose nodes are the assets composing it. The weights on the nodes and the arcs represent the share of capital invested on the assets and the dependence among them, respectively. The risk profile of the portfolio will be given through a suitably defined riskmeasure on the portfolio-network.The standard Markowitz theory will be rewritten in this particular setting. Surprisingly, we will note that the resulting decision problem is not consistent with an adapted version of the axiomatization of the standard expected utility theory.