Statistical detection and classification of background risks affecting inputs and outputs

Abstract

Systems are exposed to a variety of risks, including those known as background or systematic risks. Therefore, advanced economic, financial, and engineering models incorporate such risks, thus inevitably making the models more challenging to explore. A number of natural questions arise. First and foremost, is the given system affected by any of such risks? If so, then is the system affected by the risks at the input or output stage, or at both stages? In the present paper we construct an algorithm that answers such questions. Even though the algorithm is based on intricate probabilistic considerations, its practical implementation is easy. Keywords

Special Issue “Risk, Ruin and Survival: Decision Making in Insurance and Finance”

“…Many engineering-related studies employ techniques in the frequency domain, while Gribkova and Zitikis (2018) pursue the task in the time domain. The latter paper is a part of the tetralogy by Gribkova and Zitikis (2018, 2019a, 2019b, 2019c who develop a comprehensive classification and testing methodology for dealing with potential effects of systemic risk on systems at their input and/or output stages. The importance of such research is due to the fact, among other reasons, that even though the decision maker may be aware of the existence of systemic risk and would thus incorporate it into the statistical model, the decision maker cannot be sure that the resulting model complexity is really justified.…”

Detecting systematic anomalies affecting systems when inputs are stationary time series

“…Note When the inputs are iid random variables, which is a very special case of the present article, anomaly detection in systems with has been studied by Gribkova and Zitikis, 30 with by Gribkova and Zitikis, 45 and with arbitrary anomalies by Gribkova and Zitikis 46 . In the present article, we extend those iid‐based results to scenarios when inputs are governed by stationary time‐series models, which is a highly important feature from the practical point of view.…”

Risk, Ruin and Survival

“…Many engineering-related studies employ techniques in the frequency domain, while pursue the task in the time domain. The latter paper is a part of the tetralogy by , 2019a, 2019b, 2019c who develop a comprehensive classification and testing methodology for dealing with potential effects of systemic risk on systems at their input and/or output stages. The importance of such research is due to the fact, among other reasons, that even though the decision maker may be aware of the existence of systemic risk and would thus incorporate it into the statistical model, the decision maker cannot be sure that the resulting model complexity is really justified.…”