Partial Observation Case

Abstract

In many situations, the guarantor or creditor will need to invest some amount of money or management time in order to obtain the information on the current position of the guaranteed party’s assets. This situation will change the program in two different dimensions: (1) the dynamics of the controlled assets’ value, y(t), and (2) the costs faced by the guarantor. Because of these auditing costs, the guarantor will be led to observe the assets’ value process, y(t), at only some optimally selected time instants. Clearly, the programs derived under full observation can no longer be used here. In the following, we approach the optimal impulse control problem in a partial observation context by analogy with the full observation programs. For this, we assume that the guaranteed party has a passive behavior, thus avoiding the need to consider the game-theoretical framework in which to find the general solution to this problem. Also, we will only discuss the solution to the impulse control problem, since for the optimal stopping problem the solution can be deducted from the former, by replacing the control costs with the stopping cost.