Asymptotic ruin probabilities for a discrete-time risk model with dependent insurance and financial risks

This contribution focuses on a discrete-time risk model in which both insurance risk and financial risk are taken into account and they are equipped with a wide type of dependence structure. We derive precise asymptotic formulas for the ruin probabilities when the insurance risk has a dominatedly varying tail. In the special case of regular variation, the corresponding formula is proved to be uniform for the time horizon.     

基于战略风险管理模式下的养老保险公司风险管理分析

战略风险管理模式是金融企业比较流行的一种全面风险管理模型。本文在分析养老保险公司业务经营及风险管理特殊性的基础上,应用战略风险管理基本思想,提出了当前形势下养老保险公司风险管理的核心问题,并对公司目前面临的风险类别、风险因素以及风险管控措施进行了分析研究。     

The proper distribution function of the deficit in the delayed renewal risk model

The main focus of this paper is to extend the analysis of ruin-related quantities to the delayed renewal risk models. First, the background for the delayed renewal risk model is introduced and a general equation that is used as a framework is derived. The equation is obtained by conditioning on the first drop below the initial surplus level. Then, we consider the deficit at ruin among many random variables associated with ruin. The properties of the distribution function (DF) of the proper deficit are examined in particular.     

Optimal reinsurance under adjustment coefficient measure in a discrete risk model based on Poisson MA(1) process

In this paper, we study the retention levels for combinations of quota-share and excess of loss reinsurance by maximizing the insurer’s adjustment coefficient, which in turn minimizes the asymptotic result of ruin probability. Assuming that the premiums are determined by the expected value principle, we consider a discrete risk model, in which a dependence structure is introduced based on Poisson MA(1) process between the claim numbers for each period. The impact of dependence parameter on the adjustment coefficient is discussed and numerical examples are provided to illustrate the results obtained in this paper.     

The surplus prior to ruin and the deficit at ruin for a correlated risk process

This paper presents an explicit characterization for the joint probability density function of the surplus immediately prior to ruin and the deficit at ruin for a general risk process, which includes the Sparre-Andersen risk model with phase-type inter-claim times and claim sizes. The model can also accommodate a Markovian arrival process which enables claim sizes to be correlated with the inter-claim times. The marginal density function of the surplus immediately prior to ruin is specifically considered. Several numerical examples are presented to illustrate the application of this result.     

政策性农业保险参与主体博弈分析及风险防范策略

本文在对政策性农业保险参与主体进行角色定位分析的基础上,剖析了政策性农业保险中政府、保险公司和农户等主体之间以及各级政府之间在不同风险状态下的利益博弈关系,探讨了政府介入政策性农业保险条件下风险补偿的博弈行为,分别从政府、商业保险公司和农户三个主体的角度提出了政策性农业保险风险的具体防范策略。     

Hierarchical structures in the aggregation of premium risk for insurance underwriting

In the valuation of the Solvency II capital requirement, the correct appraisal of risk dependencies acquires particular relevance. These dependencies refer to the recognition of risk diversification in the aggregation process and there are different levels of aggregation and hence different types of diversification. For instance, for a non-life company at the first level the risk components of each single line of business (e.g. premium, reserve, and CAT risks) need to be combined in the overall portfolio, the second level regards the aggregation of different kind of risks as, for example, market and underwriting risk, and finally various solo legal entities could be joined together in a group.

Solvency II allows companies to capture these diversification effects in capital requirement assessment, but the identification of a proper methodology can represent a delicate issue. Indeed, while internal models by simulation approaches permit usually to obtain the portfolio multivariate distribution only in the independence case, generally the use of copula functions can consent to have the multivariate distribution under dependence assumptions too.

However, the choice of the copula and the parameter estimation could be very problematic when only few data are available. So it could be useful to find a closed formula based on Internal Models independence results with the aim to obtain the capital requirement under dependence assumption.

A simple technique, to measure the diversification effect in capital requirement assessment, is the formula, proposed by Solvency II quantitative impact studies, focused on the aggregation of capital charges, the latter equal to percentile minus average of total claims amount distribution of single line of business (LoB), using a linear correlation matrix.

On the other hand, this formula produces the correct result only for a restricted class of distributions, while it may underestimate the diversification effect.

In this paper we present an alternative method, based on the idea to adjust that formula with proper calibration factors (proposed by Sandström (2007)) and appropriately extended with the aim to consider very skewed distribution too.

In the last part considering different non-life multi-line insurers, we compare the capital requirements obtained, for only premium risk, applying the aggregation formula to the results derived by elliptical copulas and hierarchical Archimedean copulas.     

Ruin time and aggregate claim amount up to ruin time for the perturbed risk process

We consider the classical Sparre-Andersen risk process perturbed by a Wiener process, and study the joint distribution of the ruin time and the aggregate claim amounts until ruin by determining its Laplace transform. This is first done when the claim amounts follow respectively an exponential/Phase-type distribution, in which case we also compute the distribution of recovery time and study the case of a barrier dividend. Then the general distribution is considered when ruin occurs by oscillation, in which case a renewal equation is derived.     

Parisian types of ruin probabilities for a class of dependent risk-reserve processes

For a rather general class of risk-reserve processes, we provide an exact method for calculating different kinds of ruin probabilities, with particular emphasis on variations over Parisian type of ruin. The risk-reserve processes under consideration have, in general, dependent phase-type distributed claim sizes and inter-arrivals times, whereas the movement between claims can either be linear or follow a Brownian motion with linear drift. For such processes, we provide explicit formulae for classical, Parisian and cumulative Parisian types of ruin (for both finite and infinite time horizons) when the clocks are phase-type distributed. An erlangization scheme provides an efficient algorithmic methods for calculating the aforementioned ruin probabilities with deterministic clocks. Special attention is drawn to the construction of specific dependency structures, and we provide a number of numerical examples to study its effect on probabilities.