A multiperiod model for estimating the cost of deposit insurance under the Basel III minimum capital requirement

Under the Basel III regime, a commercial bank is considered adequately capitalized if it maintains a ratio of capital to total risk-weighted assets or capital adequacy ratio (CAR) of at least 8%. We model a commercial bank that complies with Basel III's minimum capital requirement on an interval $[0,T]$ for $T>0$. The bank model is achieved via a specific rate of capital influx that fixes the bank's CAR at the minimum prescribed level of 8%. On the basis of this capital influx rate, we derive models for the bank's asset portfolio and capital dynamics required for maintaining the CAR at the minimum prescribed level. For the aforementioned bank, we further study a deposit insurance (DI) pricing problem with a coverage horizon equal to $T$ years. More specifically, we employ a multiperiod DI pricing model to approximate the cost of DI for the bank on the interval $[0,T]$, where the constant (minimum) CAR is maintained. We study the behaviours of the models leading to the constant (minimum) CAR, and the behaviour of the DI premium estimate by means of numerical simulations. In the simulation study pertaining to the DI premium estimate specifically, we determine the effects of changes in the bank's initial leverage level (deposit-to-asset ratio), the DI coverage horizon, and the volatility of the asset portfolio on the DI premium estimate.     

A premium principle based on the g-integral

A novel approach of calculating an insurance premium based on g-integrals and interval-valued integrals is introduced. The characterization theorem for the g-integral-based premium principle is proven, and the relations with some well-known premium principles are discussed. The main properties of the interval-valued premium principle based on the g-integral are presented and some illustrative examples are given.     

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与经典Cramer-Lundberg风险模型中保费收取过程 是时间的线性函数不同, 我们考虑聚合的保费收取过程是复合Poisson过程, 研究了在此模型下的常数分红策略问题. Dickson和Waters,(2004)指出在破产发生时, 股东还应有责任偿付破产时的赤字. 因此, 在本文中考虑的最优准则是最大化破产发生前的分红折现值与破产发生时赤字的差的期望. 做为例子, 当个体保费收取额和索赔额均为指数分布时, 给出了计算分红障碍的条件     

The uncertainties about the relationships risk–return–volatility in the Spanish stock market

The relationships between the market risk premium, its conditional variance and the risk-free rate in the Spanish stock market are studied in this paper. Using daily data, the above mentioned relations are analyzed by quasi maximum likelihood for an EGARCH-M(1,1) model with normal innovations and by nonparametric maximum likelihood for a semiparametric EGARCH-M(1,1) model with arbitrarily distributed innovations. It is worth mentioning that the conclusions differ from one model to the other.     

认股权证的保险精算定价

引入Mogens Bladt和Tina Hviid Rydberg在无市场假设下关于期权定价的保险精算方法,利用公平保费原则和价格过程的实际概率测度,建立认股权证的定价模型,并给出定价公式.当投资者对原生资产期望回报率为无风险利率时,该定价为风险中性价格.     

Sensitivity analysis of the moments of the profit on an Income Protection Policy

The main purpose of this paper is to perform a sensitivity analysis where we quantify and analyse the effects on the mean of the profit on an Income Protection policy and two risk measures of changing the values of the transition intensities. All the calculations carried out are based on a multiple state model for Income Protection proposed in Continuous Mortality Investigation Committee (Continuous Mortality Investigation Reports 1991; 12 ). Within this model, we derive a formula for the mean of the profit, which enables to evaluate it more efficiently. In order to calculate the two risk measures we use the numerical algorithms for the calculation of the moments of the profit proposed by Waters (Insurance: Mathematics and Economics 1990; 9 :101–113). We carry out the sensitivity analysis considering two different situations: in the first situation, we update the premium rates used to calculate the moments of the profit, according to the changes in the values of the transition intensities; in the second one, we do not update the premium rates. Both analyses are of practical interest to insurance companies selling Income Protection policies. Copyright © 2009 John Wiley & Sons, Ltd.     

Estimating the distortion parameter of the proportional hazards premium for heavy-tailed losses under Lévy-stable regime

Estimating the distorted parameter in the case of non negative heavy-tailed losses has been treated in Brahimi et al. (2011). In this paper, we extend this work to the case of the real heavy-tailed losses. We derive an asymptotic distribution of the estimator. We construct a practically implemented confidence interval for the distortion parameter and illustrate the performance of the interval in a simulation study with application to real data.     

Optimal risk transfer for agents with germs

We introduce a new class of risk measures called generalized entropic risk measures (GERMS) that allow economic agents to have different attitudes towards different sources of risk. We formulate the problem of optimal risk transfer in terms of these risk measures and characterize the optimal transfer contract. The optimal contract involves what we call intertemporal source-dependent quotient sharing, where agents linearly share changes in the aggregate risk reserve that occur in response to shocks to the system over time, with scaling coefficients that depend on the attitudes of each agent towards the source of risk causing the shock. Generalized entropic risk measures are not dilations of a common base risk measure, so our results extend the class of risk measures for which explicit characterizations of the optimal transfer contract can be found.     

有随机投资回报的随机保费模型的渐近破产概率(英文)

本文研究了随机投资回报环境下扰动的随机保费模型的破产问题.利用鞅方法和随机分析的理论讨论了盈余过程的一些基本性质,得到了一个可以用来求解破产时刻的Laplace变换的积分微分方程,结果推广了已有的随机投资问报风险模型的结论.