# Optimal Insurance Policies in the Presence of Costs

## Abstract

**:**

## 1. Introduction

## 2. Insurance with Costly Claim Settlement

## 3. Pareto Optimal Deductibles in the Presence of Quasi-Fixed Costs

**Theorem**

**1.**

## 4. Constrained Pareto Optimal Contracts with Caps: XL-Reinsurance Contracts

**Theorem**

**2.**

## 5. Related Background Material

#### 5.1. The Theory of Pure Demand

#### 5.2. The Theory of Pure Supply

**Theorem**

**3.**

**Remark**

**1.**

**Theorem**

**4.**

**Example**

**1.**

**Example**

**2.**

#### 5.3. Upper Limit Policies and Insurance Costs

**Theorem**

**5.**

## 6. Conclusions

## Acknowledgments

## Conflicts of Interest

## Appendix A. Proofs of Theorems 1 and 2

**Proof**

**of**

**Theorem**

**1.**

**Proof**

**of**

**Theorem**

**2.**

## Appendix B. Proofs of Theorems 3–5

**Proof**

**of**

**Theorem**

**3.**

**Proof**

**of**

**Theorem**

**4.**

**Proof**

**of**

**Theorem**

**5.**

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1. |

x | 0 | 1 | 2 |
---|---|---|---|

P(X = x) | $\frac{1}{3}$ | $\frac{1}{3}$ | $\frac{1}{3}$ |

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**MDPI and ACS Style**

Aase, K.K.
Optimal Insurance Policies in the Presence of Costs. *Risks* **2017**, *5*, 46.
https://doi.org/10.3390/risks5030046

**AMA Style**

Aase KK.
Optimal Insurance Policies in the Presence of Costs. *Risks*. 2017; 5(3):46.
https://doi.org/10.3390/risks5030046

**Chicago/Turabian Style**

Aase, Knut K.
2017. "Optimal Insurance Policies in the Presence of Costs" *Risks* 5, no. 3: 46.
https://doi.org/10.3390/risks5030046