Decision Making Under Uncertainty With Applications To Geosciences And Finance

In many practical situations, we need to make a decision. In engineering, we need to decide on the best design of a system, and, for existing systems â?? on the best control strategy. In financial applications, we need to decide what is the best way to invest money. In geosciences, we need to decide whether we should explore a possible mineral deposit â?? or whether we should perform more experiments and measurements (and what exactly). In some cases, we can compute the exact consequences of each decision - e.g., if we are controlling a satellite. However, in many other cases, we do not know the exact conse- quences. In such situations, we need to make a decision under uncertainty. In many application areas, uncertainty is small - and can be made even smaller by appropriate measurements. For example, when we control a self-driving car, if there is an uncertainty about the locations and speeds of other objects on the road, we can install more accurate sensors and get a better description of the driving environment. However, there are applications when it is difficult or even impossible to decrease un- certainty. One such area is anything related to human activities. Humans make individual decisions based on their perceived value of different alternatives. The same alternative â?? be it a movie or a computer - have drastically different value to different people, so it is very difficult to predict their behavior. Such behavior affects economics and finance, so in decision making in economics and finance, it is very important to take such decision making under uncertainty into account. Another area where it is difficult to decrease uncertainty is geosciences. In this Thesis, we analyze the general problem of decision making under uncertainty and show how our results can be applied to finances and geosciences