Some aspects of decision making under uncertainty

Two discrete-time insurance models are studied in the framework of cost approach. The models being non-deterministic one deals with decision making under uncertainty. Three different situations are investigated: (1) underlying processes are stochastic however their probability distributions are given; (2) information concerning the distribution laws is incomplete; (3) nothing is known about the processes under consideration: Mathematical methods useful for establishing the (asymptotically) optimal control are demonstrated in each case. Algorithms for calculation of critical levels are proposed. Numerical results are presented as well. (c) 2007 Elsevier B.V. All rights reserved.