A User-Friendly Algorithm for Detecting the Influence of Background Risks on a Model

Abstract

Background, or systematic, risks are integral parts of many systems and models in insurance and finance. These risks can, for example, be economic in nature, or they can carry more technical connotations, such as errors or intrusions, which could be intentional or unintentional. A most natural question arises from the practical point of view: is the given system really affected by these risks? In this paper we offer an algorithm for answering this question, given input-output data and appropriately constructed statistics, which rely on the order statistics of inputs and the concomitants of outputs. Even though the idea is rooted in complex statistical and probabilistic considerations, the algorithm is easy to implement and use in practice, as illustrated using simulated data.

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.…”