Precise large deviation result for heavy-tailed random sums and applications to risk theory

The differences between two sequences of nonnegative independent and identically distributed random variables with sub-exponential tails and the random index are studied. The random index is a strictly stationary renewal counting process generated by some negatively associated random variables. Using a revised large deviation result of partial sums, the elementary renewal theorem and the central limit theorem of negatively associated random variables, a precise large deviation result is derived for the random sums. The result is applied to the customer-arrival-based insurance risk model. Some uniform asymptotics for the ruin probabilities of an insurance company are obtained as the number of customers or the time tends to infinity.

Evolution of seismic risk management for insurance over the past 30 years

During the past 30 years, there has been spectacular growth in the use of risk analysis and risk management tools developed by engineers in the financial and insurance sectors. The insurance, the reinsurance, and the investment banking sectors have enthusiastically adopted loss estimation tools developed by engineers in developing their business strategies and for managing their financial risks. As a result, insurance/reinsurance strategy has evolved as a major risk mitigation tool in managing catastrophe risk at the individual, corporate, and government level. This is particularly true in developed countries such as US, Western Europe, and Japan. Unfortunately, it has not received the needed attention in developing countries, where such a strategy for risk management is most needed. Fortunately, in the last five years, there has been excellent focus in developing ＂Insur Tech＂ tools to address the much needed ＂Insurance for the Masses＂, especially for the Asian Markets. In the earlier years of catastrophe model development, risk analysts were mainly concerned with risk reduction options through engineering strategies, and relatively little attention was given to financial and economic strategies. Such state-of-affairs still exists in many developing countries. The new developments in the science and technologies of loss estimation due to natural catastrophes have made it possible for financial sectors to model their business strategies such as peril and geographic diversification, premium calculations, reserve strategies, reinsurance contracts, and other underwriting tools. These developments have not only changed the way in which financial sectors assess and manage their risks, but have also changed the domain of opportunities for engineers and scientists.This paper will address the issues related to developing insurance/reinsurance strategies to mitigate catastrophe risks and describe the role catastrophe risk insurance and reinsurance has played in managing financial risk due to natural catastrophes. Historical losses and the share of those losses covered by insurance will be presented. How such risk sharing can help the nation share the burden of losses between tax paying public, the ＂at risk＂ property owners, the insurers and the reinsurers will be discussed. The paper will summarize the tools that are used by the insurance and reinsurance companies for estimating their future losses due to catastrophic natural events. The paper will also show how the results of loss estimation technologies developed by engineers are communicated to the business flow of insurance/reinsurance companies. Finally, to make it possible to grow ＂Insurance for the Masses - IFM＂, the role played by parametric insurance products and Insur Tech tools will be discussed.

Ruin Probability of One Kind of Entrance Processes Based Insurance Risk Models

In this note,one kind of insurance risk models with the policies having multiple validity times are investigated.Explicit expressions for the ruin probabilities are obtained by using the martingale method.As a consequence,the obtained probability serves as an upper bound for the ruin probability of a newly developed entrance processes based risk model.

The Mathematical Analysis on the Risk Management Effect of Crop Insurance Plan

As a variant index, variation has an inherent shortcoming that it can only reflect the static fluctuation of the crop. This paper makes complementary analysis about it on the basis of the comment on Miranda＇s approach of β index and goes on to analyze the β index approach under the condition of three kinds of crop insurance plans, β index approach has the advantage that it can dynamically reflect the risk transfer effect of crop insurance plan. At the same insurance level, the smaller the β index is, the better the corresponding risk transfer effect of crop insurance plan is; And vice versa.

Evolution of research on climate risk insurance:A bibliometric analysis from 1975 to 2022

Insurance against climate risk is essential for mitigating the adverse effects of climate change.However,theoretical consensus regarding climate risk insurance remains elusive,and the implementation of climate insurance policies varies markedly between countries owing to various challenges.This study conducted bibliometric analysis of 1082 relevant publications(1975–2022)to determine the theoretical basis,evolution of research hotspots,and methodologies associated with climate risk insurance.Climate insurance publications are growing at an average annual rate of 8.9%,with more than 2333 authors from 1103 organizations in 78 countries publishing on the subject.On the basis of milestones of global climate change assessment,i.e.,the publication of the Fourth and Fifth Assessment Reports of the Intergovernmental Panel on Climate Change,climate insurance research can be divided into three major phases.In the start-up phase(1975–2007),research schemes examined the feasibilities and potentials of the National Flood Insurance Program in the United States,and the socioeconomic implications of transferring climate risk through reinsurance.The methodologies used in these studies were relatively simple owing to lack of comprehensive data.Research on flood insurance increased rapidly during the development phase(2008–2014),with increasing emphasis on the possibility of developing a flood insurance market in the Netherlands.Studies utilized catastrophe modeling and probabilistic approaches to estimate natural disaster losses and financial impacts.The boom phase(2015–2022)involved more research on the affordability of climate risk insurance given income inequality.The topic of climate insurance and the scope of its impact have developed global and interdisciplinary characteristics in terms of journal,sector,and disciplinary base.In the future,a trend might develop whereby big data will be combined with artificial intelligence and machine learning to design and implement index insurance.

Asymptotics for the joint tail probability of bidimensional randomly weighted sums with applications to insurance

This paper studies the joint tail behavior of two randomly weighted sums∑_(i=1)^(m)Θ_(i)X_(i)and∑_(j=1)^(n)θ_(j)Y_(j)for some m,n∈N∪{∞},in which the primary random variables{X_(i);i∈N}and{Y_(i);i∈N},respectively,are real-valued,dependent and heavy-tailed,while the random weights{Θi,θi;i∈N}are nonnegative and arbitrarily dependent,but the three sequences{X_(i);i∈N},{Y_(i);i∈N}and{Θ_(i),θ_(i);i∈N}are mutually independent.Under two types of weak dependence assumptions on the heavy-tailed primary random variables and some mild moment conditions on the random weights,we establish some(uniformly)asymptotic formulas for the joint tail probability of the two randomly weighted sums,expressing the insensitivity with respect to the underlying weak dependence structures.As applications,we consider both discrete-time and continuous-time insurance risk models,and obtain some asymptotic results for ruin probabilities.

Agricultural Risk Modeling Challenges in China:Probabilistic Modeling of Rice Losses in Hunan Province

This article summarizes a joint research projec undertaken under the Risk Management Solutions, Inc(RMS) banner to investigate some of the possible approaches for agricultural risk modeling in China. Two modeling approaches were investigated—the simulated weather crop index and the burn yield analysis approach. The study was limited to Hunan Province and a single crop—rice. Both modeling approaches were dealt with probabilistically and were able to produce probabilistic risk metrics. Illustrative model outputs are also presented. The article discusses the robustness of the modeling approaches and their dependence on the availability, access to, and quality of weather and yield data. We offer our perspective on the requirements for models and platforms for agricultural risk quantification in China in order to respond to the needs of all stakeholders in agricultural risk transfer.

Estimates for the Finite-time Ruin Probability with Insurance and Financial Risks

The paper gives estimates for the finite-time ruin probability with insurance and financial risks. When the distribution of the insurance risk belongs to the class L（γ） for some γ〉0 or the subexponential distribution class, we abtain some asymptotic equivalent relationships for the finite-time ruin probability, respectively. When the distribution of the insurance risk belongs to the dominated varying-tailed distribution class, we obtain asymptotic upper bound and lower bound for the finite-time ruin probability, where for the asymptotic upper bound, we completely get rid of the restriction of mutual independence on insurance risks, and for the lower bound, we only need the insurance risks to have a weak positive association structure. The obtained results extend and improve some existing results.

The First Two Moments of Aggregate Claims in a Markovian Environment

We consider the discounted aggregate claims when the insurance risks and financial risks are governed by a discrete-time Markovian environment.We assume that the claim sizes and the financial risks fluctuate over time according to the states of economy,which are interpreted as the states of Markovian environment.We will then determine a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under mild assumption.Moreover,using the differentio-integral equation,we will also investigate the first two order moments of discounted aggregate claims in a Markovian environment.

A Note on Randomly Weighted Sums of Dependent Subexponential Random Variables

The author obtains that the asymptotic relations ■ hold as x→∞, where the random weights θ1,···, θn are bounded away both from 0 and from∞with no dependency assumptions, independent of the primary random variables X1,···, Xn which have a certain kind of dependence structure and follow non-identically subexponential distributions. In particular, the asymptotic relations remain true when X1,···, Xn jointly follow a pairwise Sarmanov distribution.

Customised insurance coverage for ship financiers

This article focuses on exploring what types of marine policies are appropriate for ship financiers.It considers this question from two aspects:in theory and in practice.In spite of the efficiency of transferring ship finance related risks via purchasing insurance coverage,the limitations of insurance solutions shall receive enough attention.