Ruin Problems for Phase-Type(2) Risk Processes

In this paper we consider a risk process in which claim inter-arrival times have a phase-type(2) distribution, a distribution with a density satisfying a second order linear differential equation. We consider some ruin related problems. In particular, we consider the compound geometric representation of the infinite time survival probability, as well as the (defective) distributions of the surplus immediately prior to ruin and of the deficit at ruin. We also consider explicit solutions for the infinite time ruin probability in the case where the individual claim amount distribution is phase-type.     

Forecasting and decomposition of portfolio credit risk using macroeconomic and frailty factors

This paper presents a dynamic portfolio credit model following the regulatory framework, using macroeconomic and latent risk factors to predict the aggregate loan portfolio loss in a banking system. The latent risk factors have three levels: global across the entire banking system, parent-sectoral for the intermediate loan sectors and sector-specific for the individual loan sectors. The aggregate credit loss distribution of the banking system over a risk horizon is generated by Monte Carlo simulation, and a quantile estimator is used to produce the aggregate risk measure and economic capital. The risk contributions of the individual sectors and risk factors are measured by combining the Hoeffding decomposition with the Euler capital allocation rule. For the U.S. banking system, we find that the real GDP growth rate, the global and sector-wide frailty risk factors and their spillovers significantly affect loan defaults, and the impacts of the frailty factors are not only economy-wide but also sector-specific. We also find that the frailty risk factors make more significant risk contributions to the aggregate portfolio risk than the macroeconomic factors, while the macroeconomic factors help to improve the accuracy and efficiency of the credit risk forecasts.     

Continuity Estimates for Ruin Probabilities

A method of continuity analysis of ruin probabilities with respect to variation of parameters governing risk processes is proposed. It is based on the representation of the ruin probability as the stationary probability of a reversed process. We apply Kartashov's technique designed for continuity analysis of stationary distributions of general Markov chains in order to obtain desired continuity estimates. The method is illustrated by the Sparre Andersen and Markov modulated risk models.     

PORTFOLIO CHOICE VIA QUANTILES

A portfolio choice model in continuous time is formulated for both complete and incomplete markets, where the quantile function of the terminal cash flow, instead of the cash flow itself, is taken as the decision variable. This formulation covers a wide body of existing and new models with law‐invariant preference measures, including expected utility maximization, mean–variance, goal reaching, Yaari's dual model, Lopes' SP/A model, behavioral model under prospect theory, as well as those explicitly involving VaR and CVaR in objectives and/or constraints. A solution scheme to this quantile model is proposed, and then demonstrated by solving analytically the goal‐reaching model and Yaari's dual model. A general property derived for the quantile model is that the optimal terminal payment is anticomonotonic with the pricing kernel (or with the minimal pricing kernel in the case of an incomplete market if the investment opportunity set is deterministic). As a consequence, the mutual fund theorem still holds in a market where rational and irrational agents co‐exist.     

客观现象的概率统计解释举例

本文通过应用概率统计方法解释人类行为与认识活动实例的分析,说明了基于概率统计方法如何描述客观现象和理解人类的认识行为,进而得出概率统计方法是基于归纳的演绎推理,其本质是认识论中的归纳推理。     

随机利率下的复合Poisson-Geometric风险模型及破产概率

本文主要研究的是在随机利率下保费收入为复合Poisson-Geometric过程的风险模型,在随机利率为levy过程的情况下,得到了破产概率满足的积分方程,以及得到最终破产概率的上下界所满足的积分不等式,以此作为保险公司经营的预警信号更具有现实意义。     

Loan price modelling for local governments using risk premium analysis

Previous studies have highlighted the question of government loan interest as one of great current importance. Government borrowing levels are high, and reducing interest payments would generate savings to meet other spending needs and/or to lower taxation, thus supporting the sustainability of public finances. However, no previous study has presented a method for a local government to calculate its own credit risk and thus be in a position to negotiate lower interest rates on its borrowing. This article defines a financial model that enables local governments to estimate the interest rate payable on a bank loan, based on their credit risk premium, in accordance with the Basel II rules and the findings of our empirical study of large local governments.     

Instant‐count sampling: A technique for estimating recreation use in municipal settings

Instant‐count sampling was tested on four municipal recreation areas in Athens, Georgia. Users were counted instantaneously on the areas at randomly selected times. From these counts, estimates of use and standard errors were achieved with a minimum of sampling time required. Errors ranged from 10.2 to 37.8 percent of estimated use and did not exceed 23.6 percent for total use.     

基于马尔柯夫分析的计算机预测和决策应用

从DSS应用现状出发,介绍了马尔柯夫分析的定义和数学原理,阐述了马尔柯夫分析的过程和预测的基本步骤,利用Excel设计了进行市场占有率预测的应用模型,并进行了仿真预测和决策分析。测试表明,应用模型简便通用,操作方便,提高了预测的计算精度和效率。