The risk of natural disasters has increased over the last few decades, leading to significant economic losses across the globe. In response, research related to the risk of economic loss due to natural disasters has continued to develop. At present, insurance remains the best solution for funding such losses. The purpose of this study is to analyse the development of insurance as an alternative for sustainable economic recovery after natural disasters. The data used are articles obtained from several sources indexed by Scopus and Google Scholar. The search resulted in a final database of 266 articles, culled from a total of 813 articles before the final selection was made. The articles used are publications from 2000–2021 (including 21 database periods), to which we applied a systematic literature review method. Identification and evaluation of the articles was carried out through visualization of their content, development of disaster risk insurance, and availability of disaster risk insurance by country and type. The identification results show that the relationship between the word “insurance”, according to visualization using the VOSviewer software, has a relationship with other clusters including the words “disaster”, “disaster insurance”, “risk”, “natural disaster”, “study”, “recovery”, and “disaster risk financing”. The 266 articles studied show that there was an annual increase in the number of published scientific papers over the period 2000–2021. The types of disaster risk insurance, based on a review of the articles, include agricultural insurance, flood insurance, property insurance, earthquake insurance, crop insurance, and natural disaster insurance. In addition, of the six types of disaster risk insurance, three have been discussed the most in the last five years, namely, agricultural, flood, and property insurance. The increase in the number of scientific publications discussing these three types of disaster risk insurance has been influenced by climate change. Climate change causes a significant increase in the potential for disasters and is accompanied by an increased risk of loss. This review is expected to provide information and motivation for researchers related to the development and importance of disaster risk insurance research. Research in the risk sector for disaster losses due to climate change should be continued in the future in order to help fund economic recovery, especially throughout the insurance sector. With continuous research on disaster risk insurance, it is hoped that the resulting information can be more effective in determining insurance risk and in helping local economies and communities recover after the advent of a disaster. With the availability of funds for post-disaster recovery, the regional economy affected by the disaster can be immediately restored and recovered from adversity.

Bibliometric analysis is the quantitative study of bibliographic material. In this paper, a systematic review of papers, authors, and journals is carried out. This is necessary to determine and set targets to be achieved in further research. The main objective of this study is to identify some of the most relevant research and the latest trends according to the information found in the Google Scholar, Publish or Perish, Science Direct, and Dimension databases. The methods used are classification, analysis of the most cited journals of all time, and the most prolific and influential authors. The results are information on the number of papers, citations, researchers, h-index, g-index, major reference journals, and visualization of research roadmaps for the topic of agricultural insurance mathematical models. The research findings identify the core themes, which are used as research gaps for future research.

Earthquake catastrophe bond pricing models (ECBPMs) employ extreme value theory (EVT) to predict severe losses, although studies on EVT’s use in ECBPMs are still rare. Therefore, this study aimed to use a mini-review approach (MRA) to examine the use of EVT and identify the gaps and weaknesses in the methods or models developed. The MRA stages include planning, search and selection, analysis, and interpretation of the results. The selection results showed five articles regarding the application of EVT in ECBPMs. Furthermore, the analysis found the following: First, the generalized extreme value (GEV) could eliminate extreme data in a period. Second, the trigger model using two parameters is better than one, but the study did not discuss the joint distribution of the two parameters. Third, the autoregressive integrated moving average (ARIMA) allows negative values. Fourth, Cox–Ingersoll–Ross (CIR) in-coupon modeling is less effective in depicting the real picture. This is because it has a constant volatility assumption and cannot describe jumps due to monetary policy. Based on these limitations, it is hoped that future studies can develop an ECBPM that reduces the moral hazard.

Explaining all published articles on the typhoid disease transmission model was carried out. It has been conducted to understand how Salmonella is transmitted among humans and vectors with variation interventions to control the spread of the typhoid disease. Specific objectives were to (1) identify the model developed, (2) describe the studies, and (3) identify the interventions of the model. It systemically searched and reviewed Dimension, Scopus, and ScienceDirect databases from 2013 through to 2022 for articles that studied the spread of typhoid fever through a compartmental mathematical model. This study obtained 111 unique articles from three databases, resulting in 23 articles corresponding to the created terms. All the articles were elaborated on to identify their identities for more explanation. Various interventions were considered in the model of each article, are identified, and then summarized to find out the opportunities for model development in future works. The whole article’s content was identified and outlined regarding how mathematics plays a role in model analysis and study of typhoid disease spread with various interventions. The study of mathematical modeling for typhoid disease transmission can be developed on analysis and creating the model with direct and indirect interventions to the human population for further work.

The problems of investing in financial assets are to choose a combination of weighting a portfolio can be maximized return expectations and minimizing the risk. This paper discusses the modeling of Mean-VaR portfolio optimization by risk tolerance, when square-shaped utility functions. It is assumed that the asset return has a certain distribution, and the risk of the portfolio is measured using the Value-at-Risk (VaR). So, the process of optimization of the portfolio is done based on the model of Mean-VaR portfolio optimization model for the Mean-VaR done using matrix algebra approach, and the Lagrange multiplier method, as well as Khun-Tucker. The results of the modeling portfolio optimization is in the form of a weighting vector equations depends on the vector mean return vector assets, identities, and matrix covariance between return of assets, as well as a factor in risk tolerance. As an illustration of numeric, analyzed five shares traded on the stock market in Indonesia. Based on analysis of five stocks return data gained the vector of weight composition and graphics of efficient surface of portfolio. Vector composition weighting weights and efficient surface charts can be used as a guide for investors in decisions to invest.