Discrete-Time Stochastic Models With Actuarial Applications

TUBITAK Project, 2022 - 2023

  • Project Type: TUBITAK Project
  • Begin Date: March 2022
  • End Date: March 2023

Project Abstract

Ruin theory has received significant attention over the last decades as it can be used not only to assess the risk profile, but also to determine the solvency requirements of insurance firms. Although, ruin is defined as the event that the surplus of an insurance firm will drop below the solvency capital requirements, market evidences indicate that insurance firms are allowed to spend some time in red, where actions to restore the capital are taken. In this project, we consider a generalization of the ruin concept to the concept of bankruptcy, according to which one has a positive surplus-dependent probability to continue despite temporary low surplus. The bankruptcy concept provides more information and can be used as a risk management tool for regulators and firms. Hence, we will introduce:

(a) a discrete time risk model (random walk), where the probability of bankruptcy will be calculated,

(b) as a generalized version of (a); discretized type Lévy processes which will be observed at some random times, where a new methodology will be developed for calculating first passage and exit times of the randomly observed discretized Lévy processes