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

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Model

## 3. The Algorithm

**Definition**

**1.**

**Case****1:**- The pivot ${I}_{n}$ is not approaching $1/2$.
- (i)
- If ${I}_{n}$ decisively tends to a limit other than $1/2$, then we advise the decision maker about the absence of the risk.
- (ii)
- If ${I}_{n}$ seems to tend to a limit other than $1/2$ but there is some doubt as to whether this is true, then we check if the supporter ${B}_{n}$ is asymptotically bounded, and if yes, then we advise the decision maker about the absence of the risk.

**Case****2:**- The pivot ${I}_{n}$ is approaching $1/2$.
- (i)
- If the supporter ${B}_{n}$ tends to infinity, then we advise the decision maker about the presence of the risk.
- (ii)
- If the supporter ${B}_{n}$ is asymptotically bounded, then $h(a)$ and $h(b)$ are likely to be insufficiently different to have already triggered Case 1 above, and we thus advise the decision maker about the absence of the risk.

## 4. Asymptotics of the Pivot ${\mathit{I}}_{\mathit{n}}$

**Theorem**

**1**

**.**If δ is absent, then, when $n\to \infty $, the pivot ${I}_{n}$ converges to

**Definition**

**2.**

**Example**

**1.**

## 5. Growth of the Supporter ${\mathit{B}}_{\mathit{n}}$

**Theorem**

**2.**

**Theorem**

**3.**

**Example**

**2.**

**Proof**

**of**

**Theorem**

**3.**

## 6. Concluding Notes

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Gribkova, N.; Zitikis, R.
A User-Friendly Algorithm for Detecting the Influence of Background Risks on a Model. *Risks* **2018**, *6*, 100.
https://doi.org/10.3390/risks6030100

**AMA Style**

Gribkova N, Zitikis R.
A User-Friendly Algorithm for Detecting the Influence of Background Risks on a Model. *Risks*. 2018; 6(3):100.
https://doi.org/10.3390/risks6030100

**Chicago/Turabian Style**

Gribkova, Nadezhda, and Ričardas Zitikis.
2018. "A User-Friendly Algorithm for Detecting the Influence of Background Risks on a Model" *Risks* 6, no. 3: 100.
https://doi.org/10.3390/risks6030100