CORE
🇺🇦
make metadata, not war
Services
Services overview
Explore all CORE services
Access to raw data
API
Dataset
FastSync
Content discovery
Recommender
Discovery
OAI identifiers
OAI Resolver
Managing content
Dashboard
Bespoke contracts
Consultancy services
Support us
Support us
Membership
Sponsorship
Community governance
Advisory Board
Board of supporters
Research network
About
About us
Our mission
Team
Blog
FAQs
Contact us
Risk models with capital injections
Authors
Marjan Qazvini
Publication date
1 January 2016
Publisher
Abstract
© 2016 Dr. Marjan QazviniOne of the main issues in ruin theory is that existing formulae for continuous time models can only be applied to some special claim size distributions and the analytical expressions for other claim size distributions do not exist. This thesis addresses this issue by considering discrete time models as approximations to continuous time models, including the classical risk model, the Markov-modulated risk model and the classical risk model with dividends. It also shows that how these models are affected by the introduction of capital injections. In Chapters 3 and 4 we construct a Gerber-Shiu function and use this to analyse the classical risk model with capital injections both analytically and probabilistically. Quantities such as the ultimate ruin probability and the joint density of the time of ruin and the number of claims until ruin are obtained by the inversion of the Laplace transform of our Gerber-Shiu function. In Chapter 5 we develop a discrete time model to approximate the probability of ruin in infinite and finite time under the classical risk model with capital injections, and show that capital injections can lead to a reduction in the probability of ruin even when claim amounts follow a heavy-tailed distribution. In Chapter 6 we extend our numerical algorithm from Chapter 5 to approximate the ultimate probability of ruin under a two-state Markov-modulated risk model with and without capital injections, and the density of the time of ruin under the same model with more than two states. The final chapter investigates dividend strategies with capital injections. We examine the effect of capital injections on the barrier and threshold strategies and consider a reinsurance arrangement that covers any fall below a positive pre-determined surplus level, so that the insurance company may operate indefinitely
Similar works
Full text
Open in the Core reader
Download PDF
Available Versions
University of Melbourne Institutional Repository
See this paper in CORE
Go to the repository landing page
Download from data provider
oai:jupiter.its.unimelb.edu.au...
Last time updated on 06/01/2019