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.

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.

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.

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.

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.