The Model

Abstract

The general model we propose could be applied to a wide range of specific situations, for the control of credit risk or of any short or long position in financial guarantees. It can be used for ongoing control of guarantees (i.e., impulse control) or for optimal seizure timing (i.e., stopping time). In the real world, some situations will allow for ongoing control; others will leave only seizure as a control mean. When ongoing control is allowed, control of the guaranteed party’s assets is effected by monitoring them repeatedly (either continuously if monitoring is free or at endogenously determined time intervals) and by asking for changes in asset structure regularly (i.e., asking for new collateral, equity infusion, etc.). The program will provide both the optimal times to monitor the assets and the optimal times to control them (i.e., impact them), and will also provide the amount of changes that should be requested. When only seizure is allowed for control, control of the guaranteed party’s assets is effected by monitoring the assets repeatedly at endogenously determined optimal time intervals, which will undoubtedly differ from those of the previous situation, and by seizing the assets, hence freezing their value at time of seizure and realizing this value. The modified program (as will be briefly shown later) would then provide optimal timing for auditing as well as for the final time of seizure.