Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Ruin problems with investments on a finite interval: PIDEs and their viscosity solutions

Viktor Antipov, Yuri Kabanov

Abstract

The study deals with the ruin problem when an insurance company invests its reserve in a risky asset whose the price dynamics is given by a geometric Lévy process. Considering the ruin probability as a of the capital reserve we obtain for it a partial integro-differential equation understood in a viscosity sense and prove a result on the uniqueness of the viscosity solution for a corresponding boundary value problem.

Ruin problems with investments on a finite interval: PIDEs and their viscosity solutions

Abstract

The study deals with the ruin problem when an insurance company invests its reserve in a risky asset whose the price dynamics is given by a geometric Lévy process. Considering the ruin probability as a of the capital reserve we obtain for it a partial integro-differential equation understood in a viscosity sense and prove a result on the uniqueness of the viscosity solution for a corresponding boundary value problem.
Paper Structure (5 sections, 7 theorems, 74 equations)

This paper contains 5 sections, 7 theorems, 74 equations.

Table of Contents

  1. Introduction
  2. The model
  3. Partial integro-differential equation
  4. Parabolic jets
  5. The maximum principle and uniqueness theorem

Key Result

theorem 1

The function $\Psi(t,u)$ on $]0,T[\times ]0,\infty[$ is a viscosity solution of the partial integro-diffe-rential equation

Theorems & Definitions (9)

  • theorem 1
  • lemma thmcounterlemma
  • lemma thmcounterlemma
  • remark thmcounterremark
  • lemma thmcounterlemma
  • lemma thmcounterlemma
  • remark thmcounterremark
  • theorem 2
  • theorem 3