Decision making with imprecise probabilities and utilities by means of statistical preference and stochastic dominance

A problem of decision making under uncertainty in which the choice must be made between two sets of alternatives instead of two single ones is considered. A number of choice rules are proposed and their main properties are investigated, focusing particularly on the generalizations of stochastic dominance and statistical preference. The particular cases where imprecision is present in the utilities or in the beliefs associated to two alternatives are considered.     

Impulse control of pension fund contributions,in a regime switching economy

In defined benefit pension plans, allowances are independent from the financial performance of the fund. And the sponsoring firm pays regularly contributions to limit deviations of fund assets from the mathematical reserve, necessary for covering the promised liabilities. This research paper proposes a method to optimize the timing and size of contributions, in a regime switching economy. The model takes into consideration important market frictions, like transactions costs, late payments and illiquidity. The problem is solved numerically using dynamic programming and impulse control techniques. Our approach is based on parallel grids, with trinomial links, discretizing the asset return in each economic regime.     

Maximum Lebesgue extension of monotone convex functions

Given a monotone convex function on the space of essentially bounded random variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables as possible. We show that there exists a maximum such extension, with explicit construction, where the maximum domain of extension is obtained as a (possibly proper) subspace of a natural Orlicz-type space, characterized by a certain uniform integrability property. As an application, we provide a characterization of the Lebesgue property of monotone convex function on arbitrary solid spaces of random variables in terms of uniform integrability and a “nice” dual representation of the function.     

Borch’s Theorem from the perspective of comonotonicity

This short note revisits the classical Theorem of Borch on the characterization of Pareto optimal risk exchange treaties under the expected utility paradigm. Our objective is to approach the optimal risk exchange problem by a new method, which is based on a Breeden–Litzenberger type integral representation formula for increasing convex functions and the theory of comonotonicity. Our method allows us to derive Borch’s characterization without using Kuhn–Tucker theory, and also without the need of assuming that all utility functions are continuously differentiable everywhere. We demonstrate that our approach can be used effectively to solve the Pareto optimal risk-sharing problem with a positivity constraint being imposed on the admissible allocations when the aggregate risk is positive.     

Asymptotic finite-time ruin probability for a bidimensional renewal risk model with constant interest force and dependent subexponential claims

This paper considers a bidimensional renewal risk model with constant interest force and dependent subexponential claims. Under the assumption that the claim size vectors form a sequence of independent and identically distributed random vectors following a common bivariate Farlie–Gumbel–Morgenstern distribution, we derive for the finite-time ruin probability an explicit asymptotic formula.     

Solvency II,regulatory capital,and optimal reinsurance: How good are Conditional Value-at-Risk and spectral risk measures?

We study the problem of optimal reinsurance as a means of risk management in the regulatory framework of Solvency II under Conditional Value-at-Risk and, as its natural extension, spectral risk measures. First, we show that stop-loss reinsurance is optimal under both Conditional Value-at-Risk and spectral risk measures. Spectral risk measures thus constitute a more general class of suitable regulatory risk measures than specific Conditional Value-at-Risk. At the same time, the established type of stop-loss reinsurance can be maintained as the optimal risk management strategy that minimizes regulatory capital. Second, we derive the optimal deductibles for stop-loss reinsurance. We show that under Conditional Value-at-Risk, the optimal deductible tends towards restrictive and counter-intuitive corner solutions or “plunging”, which is a serious objection against its use in regulatory risk management. By means of the broader class of spectral risk measures, we are able to overcome this shortcoming as optimal deductibles are now interior solutions. Especially, the recently discussed power spectral risk measures and the Wang risk measure are shown to avoid any plunging. They yield a one-to-one correspondence between the risk parameter and the optimal deductible and, thus, provide economically plausible risk management strategies.     

On the non existence of unbiased estimators of risk for spherically symmetric distributions

We study existence of unbiased estimators of risk for estimators of the location parameter of a spherically symmetric distribution, when a residual vector is available to estimate scale, under invariant quadratic loss. We show such existence often characterizes normality.     

折现率离散时间风险模型下最大赤字问题

在引入折现率的条件下研究离散时间风险模型,运用递推方法和全概率公式,得到了破产前盈余,破产后赤字以及它们的联合分布所满足的微分积分方程,作为推论得到了破产概率所满足的微积分方程并得出结论.     

连锁超市供应链风险评价模型及实证研究

随着经济的飞速发展,供应链风险管理问题越来越受到企业的重视．但国内外还缺乏对连锁超市供应链风险的深入研究．事实上,很多连锁超市的供应链上很多环节并不完善．本文分析了连锁超市供应链上所面临的风险,构建了连锁超市供应链风险评价模型,以某连锁超市为例,通过调查问卷与所得数据,并利用熵权法确定了各指标的权重,最后基于模糊综合评价法得出的结果,提出了降低连锁超市供应链风险的对策建议．     

Multivariate risk models under heavy‐tailed risks

In this paper, we consider four common types of ruin probabilities for a discrete‐time multivariate risk model, where the insurer is assumed to be exposed to a vector of net losses resulting from a number of business lines over each period. By assuming a large initial capital for the risk model and regularly varying distributions for the net losses, we establish some interesting asymptotic estimates for ruin probabilities in terms of the upper tail dependence function of the net loss vector. Our results insightfully characterize how the dependence structure among the individual net losses affect the ruin probabilities in an asymptotic sense, and more importantly, from our main results, explicit asymptotic estimates for those ruin probabilities can be obtained via specifying a copula for the net loss vectors. Copyright © 2013 John Wiley & Sons, Ltd.