The time of ultimate recovery in Gaussian risk model

三季节离散风险模型的破产概率

Ruin probability in the three-seasonal discrete-time risk model

本文研究索赔额为非同分布的离散时间风险模型。我们假设索赔在三个单位的时间段内重复，即索赔分布在时间$\{1,4,7,\ldots\}$、时间$\{2,5,8,\ldots\}$和时间$\{3,6,9,\ldots\}$重合。给出了计算有限时间破产概率和最终破产概率的递推公式。我们通过几个数值例子来说明理论结果。

Multi seasonal discrete time risk model revisited

In this work we set up the distribution function of $\mathcal{M}:=\sup_{n\geqslant1}\sum_{i=1}^{n}{(Z_i-1)}$, where the random walk $\sum_{i=1}^{n}Z_i, n\in\mathbb{N},$ is generated by $N$ periodically occurring distributions and the integer-valued and non-negative random variables $Z_1,\,Z_2,\,\ldots$ are independent. The considered random walk generates so-called multi seasonal discrete time risk model, and a known distribution of random variable $\mathcal{M}$ enables to calculate ultimate time ruin or survival probability. Verifying obtained theoretical statements we demonstrate several com…

具有相依相位型理赔的风险过程的破产问题

Ruin problems for risk processes with dependent phase-type claims

本文研究具有相依非同分布相位型理赔的连续时间风险过程，提出易于刻画的分布类并结合马尔可夫调制流体嵌入技术，获得了破产时间、破产赤字及理赔次数联合分布的递归程序与破产概率界限。

On $\mathbf{2\times2}$ determinants originating from survival probabilities in homogeneous discrete time risk model

We analyze $2\times 2$ Hankel-like determinants $D_n$ that arise in the initial values problem for the ultimate time survival probability $φ(u)$ in a homogeneous discrete time risk model $W(n)=u+κn+\sum_{i=1}^nZ_i$, where $Z_i$ are positive integer valued i.i.d. random claims, the initial surplus $u \in \mathbb{N}_0$ and the income rate $κ=2$. We prove the asymptotic version of a recent conjecture on the non--vanishing and monotonicity of $D_n$ and derive explicit formulas for the initial values $φ(0)$, $φ(1)$ of a recurrence that yields survival probabilities. In cases when $Z_i$ are Bernoull…

一般离散风险模型中基于矩指标的破产概率的渐近性

Asymptotic behaviour of ruin probabilities in a general discrete risk model using moment indices

研究了离散环境下一般经济风险模型的粗糙渐近性态。金融和保险风险都考虑在内。在第一个$n$年期间的损失被建模为随机变量$B_1+A_1B_2+\ldots+A_1\ldots A_{n-1}B_n$，其中$A_i$分别对应于$i$年的金融风险和$B_i$代表保险风险。同一年$i$的风险不被假设为独立的。主要结果表明，破产概率在一般假设下呈幂律衰减。我们的目标是给出一个完整的特征的相关量，描述的速度，破产概率消失的初始资本的数量的增长。这些量可以表示为合适的随机变量的最大矩，称为矩指数。除了对最终破产的研究外，还考虑了有限时间区间破产的情形。这两个调查广泛使用的新特性的时刻指数在上半年的文件。

Approximations to ultimate ruin probabilities with a Wienner process perturbation

In this paper, we adapt the classic Cramér-Lundberg collective risk theory model to a perturbed model by adding a Wiener process to the compound Poisson process, which can be used to incorporate premium income uncertainty, interest rate fluctuations and changes in the number of policyholders. Our study is part of a Master dissertation, our aim is to make a short overview and present additionally some new approximation methods for the infinite time ruin probabilities for the perturbed risk model. We present four different approximation methods for the perturbed risk model. The first method is b…

二维风险过程从象限的退出问题：精确和渐近结果

Exit problem of a two-dimensional risk process from the quadrant: Exact and asymptotic results

考虑两家保险公司（或同一家公司的两家分支机构），它们按照一定的比例分配索赔和保费。我们根据更新过程对索赔的发生进行建模。一个破产问题被认为是相应的二维风险过程首先离开正象限，另一个是进入负象限。当索赔按泊松过程到达时，我们得到了最终破产概率的封闭形式表达式。在一般情形下，在索赔额分布为Cramér轻尾假设下，分析了当两个公司的初始准备金趋于无穷大时破产概率的渐近性.

Noisy linear inverse problems under convex constraints: Exact risk asymptotics in high dimensions

In the standard Gaussian linear measurement model $Y=Xμ_0+ξ\in \mathbb{R}^m$ with a fixed noise level $σ>0$, we consider the problem of estimating the unknown signal $μ_0$ under a convex constraint $μ_0 \in K$, where $K$ is a closed convex set in $\mathbb{R}^n$. We show that the risk of the natural convex constrained least squares estimator (LSE) $\hatμ(σ)$ can be characterized exactly in high dimensional limits, by that of the convex constrained LSE $\hatμ_K^{\mathsf{seq}}$ in the corresponding Gaussian sequence model at a different noise level. The characterization holds (uniformly) for risk…

违约风险下的一般动态期限结构

General dynamic term structures under default risk

我们考虑的问题建模的期限结构的违约债券，在最小的假设下的违约时间。特别是，我们不假设存在违约强度，因此我们允许在可预测的时间违约的可能性。事实证明，这需要在希思、贾罗和莫顿（Heath，Jarrow and Morton，1992）的远期利率方法中引入一个附加项。这个术语是由一个随机度量驱动的，该度量编码了关于违约概率为正的时间的信息。在此框架下，我们得到了一个参考概率测度是局部鞅测度的信用风险债券的大型金融市场，也考虑一般的恢复计划的必要条件和充分条件。

高斯因子模型下贷款组合的经济资本、风险价值和Greeks的快速计算

Fast Computation Of the Economic Capital, the Value at Risk and the Greeks of a Loan Portfolio in the Gaussian Factor Model

本文提出了一种计算高斯因子模型中经济资本、风险价值和希腊数的快速算法。这里提出的算法比蛮力蒙特卡罗模拟或基于傅里叶变换的方法\cite{MD}快得多。虽然Hull-White \cite{HW}的算法非常快，但它假设投资组合中的所有贷款都具有相同的名义利率和回收率。这是一个非常严格的假设，对于实践中遇到的许多投资组合来说是不现实的。我们的算法没有假设投资组合的同质性。此外，它比Hull-White算法更容易实现。我们使用隐函数定理来推导希腊人的解析表达式。