A Splitting Method for Band Control of Brownian Motion: With Application to Mutual Reserve Optimization

Abstract

As well studied in the operations research literature, optimization of a mutual reserve system (e.g., federal reserves) and a nonmutual one such as regular inventory systems requires solving simultaneous systems of quasi-variational inequalities, of which analytical solutions in closed form remain unattainable and computational solutions are still intractable. Thus far, the studies of reserve optimization are of intra-nations (e.g., central bank reserves) as opposed to inter-nations (e.g., COVID vaccine reserves of the United Nations). In this paper, we advance a method of computational analytics for mutual reserve optimization, with an international perspective in response to the intensifying challenge on global medical reserves during the COVID pandemic. A solution algorithm is developed in the context of maritime mutual insurances (a long existent international mutual reserve system) and then tested through comprehensive numerical experiments.