# Numerical Ruin Probability in the Dual Risk Model with Risk-Free Investments

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## Abstract

**:**

## 1. Introduction

## 2. The Model

**Theorem**

**1.**

**Proof.**

**Remark**

**2.**

## 3. Integral Equation Approach

**Example**

**1.**

**Example**

**2.**

**Remark**

**3.**

## 4. Numerical Scheme

**Lemma**

**1.**

**Proof.**

**Example**

**3.**

**Example**

**4.**

**Example**

**5.**

**Example**

**6.**

## 5. The Laplace Transform of the Time of Ruin

**Theorem**

**2.**

**Proof.**

**Example**

**7.**

## 6. Conclusions and Future Research

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Exact and approximate ruin probabilities for exponential mean one gains for 10, 100, 1000 and 10,000 subintervals.

**Figure 4.**(

**a**) (Left) Ruin probabilities for various sizes of large donations, for fixed $\gamma =0.1$ and $p=0.85$. (

**b**) (Right) Ruin probabilities for various frequencies of small donations, for fixed $\gamma =0.5$ and $\beta =5$.

**Figure 5.**Laplace transform of the time of ruin for exponential mean one gains when $\delta =\frac{1}{8},\frac{1}{32},\frac{1}{128}$, 0.

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**MDPI and ACS Style**

Loke, S.-H.; Thomann, E.
Numerical Ruin Probability in the Dual Risk Model with Risk-Free Investments. *Risks* **2018**, *6*, 110.
https://doi.org/10.3390/risks6040110

**AMA Style**

Loke S-H, Thomann E.
Numerical Ruin Probability in the Dual Risk Model with Risk-Free Investments. *Risks*. 2018; 6(4):110.
https://doi.org/10.3390/risks6040110

**Chicago/Turabian Style**

Loke, Sooie-Hoe, and Enrique Thomann.
2018. "Numerical Ruin Probability in the Dual Risk Model with Risk-Free Investments" *Risks* 6, no. 4: 110.
https://doi.org/10.3390/risks6040110