Shareholder risk measures.

Summary The aim of this paper is to put forward a new family of risk measures that as the coherent/convex risk measures impose a preference order on random cash flows and can be interpreted as prices. But at the difference of the axiomatic approach of Artzner, Delbaen, Eber and Heath (1999) and the subsequent extensions of this model, our risk measures are associated with the optimal policies of shareholder value maximizing company. We study these optimal policies and the related risk measures that we call shareholder risk measures. We emphasize the fact that due to the specific corporate environment, in particular the limited shareholders’ liability and the possibility to pay out dividends from the cash reserves, these risk measures are not convex. Also, they depend on the specific economic situation of the firm, in particular its current cash level, and thus they are not translation invariant. This paper bridges the gap between two important branches of mathematical finance: risk measures and optimal dividends.