Inside the Solvency 2 Black Box: Net Asset Values and Solvency Capital Requirements with a least-squares Monte-Carlo approach

The calculation of Net Asset Values and Solvency Capital Requirements in a Solvency 2 context–and the derivation of sensitivity analyses with respect to the main financial and actuarial risk drivers–is a complex procedure at the level of a real company, where it is illusory to be able to rely on closed-form formulas. The most general approach to performing these computations is that of nested simulations. However, this method is also hardly realistic because of its huge computation resources demand. The least-squares Monte Carlo method has recently been suggested as a way to overcome these difficulties. The present paper confirms that using this method is indeed relevant for Solvency 2 computations at the level of a company.     

Modelling of insurers’ rating determinants. An application of machine learning techniques and statistical models

In recent years, financial regulations such as Basel II and Solvency II have highlighted the utility of credit risk assessments through internal rating systems, particularly for estimating the probability of default (PD) of credit exposures.     

基于灰色系统的模糊综合评判在产险公司偿付能力评价中的应用

本文将灰色系统中的灰关联分析理论和模糊数学中模糊综合评判法引入保险公司偿付能力的综合评价排序中。通过案例分析，对2005年我国八家主要财产保险公司（以下简称产险公司）的偿付能力作了判断比较，给出了综合排序。     

Risk theory insight into a zone-adaptive control strategy

The main purpose of this paper is a risk theory insight into the problem of asset-liability and solvency adaptive management. In the multiperiodic insurance risk model composed of chained classical risk models, a zone-adaptive control strategy, essentially similar to that applied in Directives [Directive 2002/13/EC of the European Parliament and of the Council of 5 March 2002, Brussels, 5 March 2002], is introduced and its performance is examined analytically. That examination was initiated in [Malinovskii, V.K., 2006b. Adaptive control strategies and dependence of finite time ruin on the premium loading. Insurance: Math. Econ. (in press)] and is based on the application of the explicit expression for the finite-time ruin probability in the classical risk model. The result of independent interest in the paper is the representation of that finite-time ruin probability in terms of asymptotic series, as time increases.     

Dividend optimization for jump–diffusion model with solvency constraints

Belhaj (2010) established that a barrier strategy is optimal for the dividend problem under jump–diffusion model. However, if the optimal dividend barrier level is set too low, then the bankruptcy probability may be too high to be acceptable. This paper aims to address this issue by taking the solvency constrain into consideration. Precisely, we consider a dividend payment problem with solvency constraint under a jump–diffusion model. Using stochastic control and PIDE, we derive the optimal dividend strategy of the problem.     

有偿付约束的无限期资产经济均衡的存在性

本文通过一个简单的模型证明了有偿付约束的无限期资产经济均衡存在性,所用条件与已有文献相比更加简明．这一研究可望为我们今后研究无限期经济提供方向：同时也可以更好地理解偿付约束（或保证金制度）在资本市场中的作用     

A dynamic equivalence principle for systematic longevity risk management

This paper addresses systematic longevity risk in long-term insurance business. We analyze the consequences of working under unknown survival probabilities on the efficiency of the Law of Large Numbers and point out the need for appropriate and feasible risk management techniques. We propose a setting for risk sharing schemes between the insurer and policyholders via a dynamic equivalence principle. We focus on a pure endowment contract and derive conditions for a viable risk sharing scheme which enhances the solvency situation of the insurer while being more favorably priced for the policyholders.     

Stochastic portfolio specific mortality and the quantification of mortality basis risk

In the last decade a vast literature on stochastic mortality models has been developed. However, these models are often not directly applicable to insurance portfolios because:

(a) For insurers and pension funds it is more relevant to model mortality rates measured in insured amounts instead of measured in the number of policies.

(b) Often there is not enough insurance portfolio specific mortality data available to fit such stochastic mortality models reliably.

Therefore, in this paper a stochastic model is proposed for portfolio specific mortality experience. Combining this stochastic process with a stochastic country population mortality process leads to stochastic portfolio specific mortality rates, measured in insured amounts. The proposed stochastic process is applied to two insurance portfolios, and the impact on the Value at Risk for longevity risk is quantified. Furthermore, the model can be used to quantify the basis risk that remains when hedging portfolio specific mortality risk with instruments of which the payoff depends on population mortality rates.     

Biometric worst-case scenarios for multi-state life insurance policies

It is common actuarial practice to calculate premiums and reserves under a set of biometric assumptions that represent a worst-case scenario for the insurer. The new solvency regime of the European Union (Solvency II) also uses worst-case scenarios for the calculation of solvency capital requirements for life insurance business. Surprisingly, the actuarial literature so far offers no exact method for the construction of biometric scenarios that let premiums and reserves be always on the safe side with respect to a given confidence band for the biometric second-order basis. The present paper partly fills this gap by introducing a general method that allows one to construct such scenarios for homogenous portfolios of life insurance policies. The results are especially informative for life insurance policies with mixed character (e.g. survival and occurrence character). Two examples are given that illustrate the new method, demonstrate its usefulness for the calculation of premiums and reserves, and show how the new approach could improve the calculation of biometric solvency reserves for Solvency II.