Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Parisian Ruin for Insurer and Reinsurer under Quota-Share Treaty

Grigori Jasnovidov, Aleksandr Shemendyuk

Abstract

In this contribution we study asymptotics of the simultaneous Parisian ruin probability of a two-dimensional fractional Brownian motion risk process. This risk process models the surplus processes of an insurance and a reinsurance companies, where the net loss is distributed between them in given proportions. We also propose an approach for simulation of Pickands and Piterbarg constants appearing in the asymptotics of the ruin probability.

Parisian Ruin for Insurer and Reinsurer under Quota-Share Treaty

Abstract

In this contribution we study asymptotics of the simultaneous Parisian ruin probability of a two-dimensional fractional Brownian motion risk process. This risk process models the surplus processes of an insurance and a reinsurance companies, where the net loss is distributed between them in given proportions. We also propose an approach for simulation of Pickands and Piterbarg constants appearing in the asymptotics of the ruin probability.

Paper Structure

This paper contains 6 sections, 8 theorems, 118 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Main Results
  3. Simulation of Piterbarg & Pickands constants
  4. Approximate values of Pickands & Piterbarg constants
  5. Proofs
  6. Appendix

Key Result

Theorem 1.1

Assume that cq holds. 1)If $t_*\notin(\overline t_1,\overline t_2)$, then as $u\to \infty$ where $i=1$ if $t_*\le \overline t_1$ and $i=2$ if $t_*\ge \overline t_2$. 2)If $t_*\in (\overline t_1,\overline t_2)$, then as $u\to \infty$ where $\mathcal{F}_{T'}^d \in (0,\infty)$ and

Figures (3)

  • Figure :
  • Figure :
  • Figure :

Theorems & Definitions (8)

  • Theorem 1.1
  • Theorem 2.1
  • Proposition 2.2
  • Lemma 3.1
  • Lemma 3.2
  • Lemma 3.3
  • Lemma 3.4
  • Proposition 5.1