Optimal liquidity allocation in an equity network

We study an optimal liquidity allocation problem in a distressed financial system when agents are embedded in a network of cross-ownership. We construct a model in which a benevolent social planner allocates a limited amount of funds to rescue agents facing liquidity shortages and whose liquidation can be avoided if the shortage is met. A discrete allocation problem arises in this setting and the "Balas" algorithm is employed to solve this problem. Solving the optimal liquidity allocation problem over a class of core-periphery equity network topologies, we establish the existence of a threshold value of exposures levels between core and peripheral nodes above which the social planner would allocate available funds to the periphery and below which to the core. The algorithm demonstrates how monetary and fiscal authorities may implement rescue plans when the size of the fund is limited and could thus serve as a new intervention tool in the arsenal of policymakers.