Risk quantification and validation for Bitcoin

This paper introduces a semi-nonparametric approach for modeling Bitcoin risk relatively to other parametric distributions and volatility models. Model performance is assessed through different backtesting techniques, including multinomial test, for three risk measures: Value-at-Risk, Expected Shortfall and Median Shortfall. Our results show that the ‘large’ semi-nonparametric expansion is a good alternative to measure Bitcoin risk according to recommendations of Basel Committee on Banking Supervision, but also that 99%-Median Shortfall seems to be an accurate and robust risk measure for Bitcoin.     

非时齐复合泊松过程下对偶风险模型的破产特征量研究

将经典的对偶风险模型中的收益到达过程推广为非时齐的泊松过程.运用经典方法和时变方法,计算了该模型下的破产概率,并定义了时变后相应模型的广义期望折罚函数,验证了时变方法对非时齐泊松风险模型的有效性,最后又考虑了该模型在带壁分红策略下的情形,当单次索赔额服从指数分布时,得到了它的期望折罚函数以及期望折现分红函数.     

常红利边界复合二项模型红利期望现值

在完全离散的复合二项风险模型基础上,考虑常红利边界策略下的红利支付问题．通过两种不同的方法,得到了红利期望现值所满足的两个方程．由这些方程特殊性质,在比较宽松的条件下,通过建立相应的迭代过程,求解出了直到破产发生时红利期望现值的近似值．     

随机收益环境下的破产时刻罚金折现期望

This paper considers the expected discounted penalty function Φ(u) for the perturbed compound Poisson risk model with stochastic return on investments. After presenting an integro-differential equation that the expected discounted penalty function satisfies, the paper derives the closed form solution by constructing an identical equation. The exact expression for Φ (0) is given using the Laplace transform technique when interest rate is constant. Applications of the results are given to the ruin probability and moments of the deficit at ruin.     

OPTIMAL PROPORTIONAL REINSURANCE WITH CONSTANT DIVIDEND BARRIER

In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then get the optimal stochastic control and the optimal constant barrier. Secondly, under the optimal constant dividend barrier strategy, we consider the moments of the discounted dividend payment and their explicit expressions are given. Finally, we discuss the Laplace transform of the time of ruin and its explicit expression is also given.     

均值-方差准则及其应用

在位置-尺度分布族中研究了均值-方差准则与期望效用理论的一致性,特别指出当均值相等时或源的支撑可达到负无穷时,均值-方差准则与期望效用理论是完全一致的,这表明可以用均值-方差准则研究满足条件的经济问题、管理问题.还介绍了均值-方差准则在金融中的一些应用.     

带随机收入离散时间风险模型的常数壁分红效用问题

考虑一类带随机收入的离散时间风险模型.通过常数分红边界的引入,考虑分红总量的期望折现以及该分红总量的期望效用.     

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or the variance parameter of the normal distribution with a normal-inverse-gamma prior, we analytically calculate the Bayes posterior estimator with respect to a conjugate normal-inverse-gamma prior distribution under Stein's loss function. This estimator minimizes the Posterior Expected Stein's Loss (PESL). We also analytically calculate the Bayes posterior estimator and the PESL under the squared error loss function. The numerical simulations exemplify our theoretical studies that the PESLs do not depend on the sample, and that the Bayes posterior estimator and the PESL under the squared error loss function are unanimously larger than those under Stein's loss function. Finally, we calculate the Bayes posterior estimators and the PESLs of the monthly simple returns of the SSE Composite Index.     

具有正态逆伽玛先验的正态分布中的方差参数在Stein损失下的贝叶斯后验估计量（英文）

对于先验分布为正态逆伽玛分布的正态分布的方差参数,我们解析地计算了具有共轭的正态逆伽玛先验分布的在Stein损失函数下的贝叶斯后验估计量.这个估计量最小化后验期望Stein损失.我们还解析地计算了在平方误差损失函数下的贝叶斯后验估计量和后验期望Stein损失.数值模拟的结果例证了我们的如下理论研究:后验期望Stein损失不依赖于样本;在平方误差损失函数下的贝叶斯后验估计量和后验期望Stein损失要一致地大于在Stein损失函数下的对应的量.最后,我们计算了上证综指的月度的简单回报的贝叶斯后验估计量和后验期望Stein损失.     

金融风险度量的建模理论与方法的一些进展及其应用

本文综述了金融风险度量的建模的理论和方法最近的发展。介绍了常用的矩度量和现代风险度量技术,包括在险价值VaR、预期不足ES和期望分位数Expectile等现代风险度量技术和方法,以及复杂风险因素下的非/半参数风险度量方法。违约概率和违约相关性是信用风险度量中的两个基本概念,本文还介绍了信用违约风险中违约概率和违约相关性的常用度量方法。最后,通过一些应用案例介绍如何在金融风险度量中应用现代风险度量技术度量和识别风险。