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The Mathematics of Pandemics: Applications for Insurance
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The Mathematics of Pandemics: Applications for Insurance

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 7332

Special Issue Editors

Dr. Carmen Boado Penas

E-Mail Website
Guest Editor
School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
Interests: actuarial mathematics; ageing; pensions; notional defined contribution accounts
Dr. Julia Eisenberg

E-Mail Website
Guest Editor
Financial & Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstr. 8/E105-1, 1040 Vienna, Austria
Interests: actuarial mathematics; stochastic optimization; optimal control theory; reinsurance, dividends, capital injections in insurance companies; optimal consumption
Special Issues, Collections and Topics in MDPI journals
Dr. Sule Sahin

E-Mail Website
Guest Editor
Actuarial Science, Department of Accounting and Finance, School for Business and Society, University of York, Heslington, York YO10 5GD, UK
Interests: actuarial mathematics; economic scenario generators; mortality modelling; actuarial compensation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In terms of financial impact, the shock to the global economy from COVID-19 has been faster and more severe than the 2008 global financial crisis and even the Great Depression. Unlike other rare events, such as tsunami or an earthquake, a pandemic can last over relatively long periods, putting severe strain on a households’ income through isolation restrictions.

This Special Issue is focused on the application of mathematics for rare events such as epidemics/pandemics so that the countries are better informed and prepared for next waves or next pandemics. We are interested in a wide range of topics, including, among others, mortality modelling and economic impact for pandemics, epidemic compartmental models, group testing, optimal strategies for lockdowns, outlier detection for pandemic-related data and design of new insurance protection products.

Dr. Carmen Boado Penas
Dr. Julia Eisenberg
Dr. Sule Sahin
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • COVID-19
  • pandemics
  • insurance mathematics
  • catastrophe risk
  • social protection

Published Papers (3 papers)

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Research

15 pages, 853 KiB  
Article
Sensitivity Analysis of Optimal Commodity Decision Making with Neural Networks: A Case for COVID-19
by Nader Karimi, Erfan Salavati, Hirbod Assa and Hojatollah Adibi
Mathematics 2023, 11(5), 1202; https://0-doi-org.brum.beds.ac.uk/10.3390/math11051202 - 28 Feb 2023
Viewed by 1053
Abstract
The COVID-19 pandemic caused a significant disruption to food demand, leading to changes in household expenditure and consumption patterns. This paper presents a method for analyzing the impact of such demand shocks on a producer’s decision to sell a commodity during economic turmoil. [...] Read more.
The COVID-19 pandemic caused a significant disruption to food demand, leading to changes in household expenditure and consumption patterns. This paper presents a method for analyzing the impact of such demand shocks on a producer’s decision to sell a commodity during economic turmoil. The method uses an artificial neural network (ANN) to approximate the optimal value function for a general stochastic differential equation and calculate the partial derivatives of the value function with respect to various parameters of both the diffusion process and the payoff function. This approach allows for sensitivity analysis of the optimal stopping problem and can be applied to a range of situations beyond just the COVID-19 crisis. Full article
(This article belongs to the Special Issue The Mathematics of Pandemics: Applications for Insurance)
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31 pages, 405 KiB  
Article
Optimal Risk Sharing in Society
by Knut K. Aase
Mathematics 2022, 10(1), 161; https://0-doi-org.brum.beds.ac.uk/10.3390/math10010161 - 05 Jan 2022
Viewed by 1764
Abstract
We consider risk sharing among individuals in a one-period setting under uncertainty that will result in payoffs to be shared among the members. We start with optimal risk sharing in an Arrow–Debreu economy, or equivalently, in a Borch-style reinsurance market. From the results [...] Read more.
We consider risk sharing among individuals in a one-period setting under uncertainty that will result in payoffs to be shared among the members. We start with optimal risk sharing in an Arrow–Debreu economy, or equivalently, in a Borch-style reinsurance market. From the results of this model we can infer how risk is optimally distributed between individuals according to their preferences and initial endowments, under some idealized conditions. A main message in this theory is the mutuality principle, of interest related to the economic effects of pandemics. From this we point out some elements of a more general theory of syndicates, where in addition, a group of people are to make a common decision under uncertainty. We extend to a competitive market as a special case of such a syndicate. Full article
(This article belongs to the Special Issue The Mathematics of Pandemics: Applications for Insurance)
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24 pages, 4641 KiB  
Article
A Macroeconomic SIR Model for COVID-19
by Erhan Bayraktar, Asaf Cohen and April Nellis
Mathematics 2021, 9(16), 1901; https://0-doi-org.brum.beds.ac.uk/10.3390/math9161901 - 10 Aug 2021
Cited by 12 | Viewed by 3276
Abstract
The COVID-19 pandemic and subsequent lockdowns highlight the close and delicate relationship between a country’s public health and economic health. Models that combine macroeconomic factors with traditional epidemic dynamics to calculate the impacts of a disease outbreak are therefore extremely useful for policymakers [...] Read more.
The COVID-19 pandemic and subsequent lockdowns highlight the close and delicate relationship between a country’s public health and economic health. Models that combine macroeconomic factors with traditional epidemic dynamics to calculate the impacts of a disease outbreak are therefore extremely useful for policymakers seeking to evaluate the best course of action in such a crisis. We developed a macroeconomic SIR model that considers herd immunity, behavior-dependent transmission rates, remote workers, and the indirect externalities of lockdowns. It is formulated as an exit time control problem where a social planner is able to prescribe separate levels of the lockdown low-risk and high-risk portions of the adult population. The model predicts that by considering the possibility of reaching herd immunity, high-risk individuals are able to leave lockdown sooner than in models where herd immunity is not considered. Additionally, a behavior-dependent transmission rate (which represents increased personal caution in response to increased infection levels) can lower both output loss and total mortality. Overall, the model-determined optimal lockdown strategy, combined with individual actions to slow virus transmission, is able to reduce total mortality to one-third of the model-predicted no-lockdown level of mortality. Full article
(This article belongs to the Special Issue The Mathematics of Pandemics: Applications for Insurance)
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