Pemaksimuman Utilitas Keuntungan Bank dengan Kontrol Optimum Stokastik

Abstract

Generally, a bank uses Basel II rules to determine how much the bank capital should be available. The capital is managed by bank as loan, provision, depository consumption, and other bank’s accomplishments. However, each allocation value may not yet maximize the value expectation of consumption utilities in specific time period and the value axpectation of profit utilities in terminal time. By using stochastic optimal conrols, the value expectation of total utilities will be maximized with three control variables, i.e. bank’s investment in loan, provision, and depository consumption. The rate of profit as constraint is in the form of stochastic differential equation, so this process is called stochastic optimal control process, with the objective function is the value expectation of the discounted total utilities in specific time period. This stochastic optimal control problem is solved by Hamilton-Jacobi-Bellman (HJB) equations