Cooperative Investment Problem With an Authoritative Risk Determined by Central Bank

Abstract

In this paper, we are interested in providing an analytic solution for cooperative investment risk. We reformulate cooperative investment risk by writing dual representations for each risk preference (Coherent risk measure). Finding an analytic solution for this problem for both cases individual and cooperative investment by using dual representation for each risk preference has a strong effect on the financial market. In addition, we formulate a problem that covers the risk minimization with an expected return maximization problem with risk constraint, for the general case of an arbitrary joint distribution for the asset return under certain conditions and assuming that all coherent risk measure is continuous from below. Thus, the optimal portfolio is written as the optimal Lagrange multiplier associated with an equality-constrained dual problem. Furthermore, a unique equilibrium allocation as a fair optimal allocation solution in terms of equilibrium price density function for each agent is also shown.