汇率风险和方差保费准则下最优投资和再保险策略

假定保险公司和再保险公司都采取方差保费准则收取保费,保险公司不但可以投资本国无风险资产和风险资产,还可以投资国外的风险资产.首先我们用一几何布朗运动来刻画汇率风险,同时为了控制保险风险,假定保险公司将承担的保险业务分保给再保险公司.接着利用随机动态规划原理研究了两种情形下的最优投资和再保险问题,一种是索赔服从扩散近似模型;另一种是经典风险模型,分别得到了这两种情形下的最优投资和再保险策略,并发现汇率风险对保险公司的投资策略有很大的影响,但对再保险策略没有影响.最后对相关参数进行了敏感性分析.     

风险相依下再保险双方的联合最优再保险问题

结合保险人和再保险人的共同利益,研究了具有两类相依险种风险模型下的最优再保险问题.假定再保险公司采用方差保费原理收取保费,利用复合Poisson模型和扩散逼近模型两种方式去刻画保险公司和再保险公司的资本盈余过程,在期望效用最大准则下,证明了最优再保险策略的存在性和唯一性,通过求解Hamilton-Jacobi-Bellman(HJB)方程,得到了两种模型下相应的最优再保险策略及值函数的明晰解答,并给出了数值算例及分析.     

风险相依下再保险双方的联合最优再保险问题

结合保险人和再保险人的共同利益,研究了具有两类相依险种风险模型下的最优再保险问题.假定再保险公司采用方差保费原理收取保费,利用复合Poisson模型和扩散逼近模型两种方式去刻画保险公司和再保险公司的资本盈余过程,在期望效用最大准则下,证明了最优再保险策略的存在性和唯一性,通过求解Hamilton-Jacobi-Bellman（HJB）方程,得到了两种模型下相应的最优再保险策略及值函数的明晰解答,并给出了数值算例及分析.     

CEV模型下最大化HARA效用的最优再保险与投资策略

在风险资产价格服从CEV模型时,考虑保险公司为最大化双曲绝对风险厌恶(HARA)效用的最优投资与再保险问题.假定保险公司的索赔过程为带漂移的布朗运动,且保险公司通过购买比例再保险来转移索赔风险,运用随机控制理论和Legendre变换方法得到了最优策略的显示表达式.     

保险公司和再保险公司之间的停止损失再保险策略选择博弈

本文在扩散逼近风险模型下考虑保险公司和再保险公司之间的停止损失再保险策略选择博弈问题.假设保险公司和再保险公司都以期望终端盈余效用增加作为购买停止损失再保险和接受承保的条件.在保险公司和再保险公司都具有指数效用函数条件下,运用动态规划原理,通过求解其对应的Hamilton-Jacobi-Bellman方程,得到了三种博弈情形下保险公司和再保险公司之间的停止损失再保险策略和值函数的显示解,以及再保险合约能够成交时再保费满足的条件.结果显示,在适当的条件下,保险公司和再保险公司之间的停止再保险合约是可以成交的.最后,通过灵敏性分析给出了最优停止损失再保险策略和再保费,以及效用损益与模型主要参数之间的关系,并给出相应的经济分析.     

基于损失规避行为的最优保险投资与再保策略选择

保险公司决策者一方面通过投资来实现保险资金的保值增值,另一方面通过再保险业务来控制承保风险.保险投资市场假定是由两种资产构成:一种是无风险资产,另一种是风险资产.与已有研究不同,文章基于累积前景理论,假定保险公司决策者具有损失规避异质性的非理性行为人.保险公司的盈余过程用跳跃扩散过程来刻画,保险公司的决策目标是最大化最终财富的"S"型期望效用,借助于鞅理论将动态的最大化问题转化为静态问题,通过求解静态优化问题得到了最优投资和再保险策略的解析表达式.数值模拟分析了最优策略的动态性质.     

方差保费准则下最优分红、注资和再保险策略

本文研究保险公司的最优分红、注资和再保险策略问题.保险公司可以通过再保险安排控制自身的风险暴露,它与再保险公司在方差保费准则下采用不同的参数进行费率定价.保险公司管理者也可以通过分红或注资控制公司资产,控制过程会消耗比例交易费和固定交易费.破产前分红现值与注资现值期望之差视为保险公司的价值.在最大化公司价值目标下,利用脉冲控制理论,本文找到最优的分红、注资和再保险策略及公司价值的最大值.     

最优再保险及投资组合策略问题

为规避风险的巨大波动,保险公司会将承保的理赔进行分保,即再保险.假定再保险公司采用方差保费准则从保险公司收取保费.应用扩散逼近模型,刻画了保险公司有再保险控制下的资本盈余.另外,保险公司的盈余允许投资到利率、股票等金融市场.通过控制再保险及投资组合策略,研究了最小破产概率.应用动态规划方法(Hamilton-Jacobi-Bellman方程),对最小破产概率、最优再保险及投资组合策略给出了明晰解答,并给出了数值直观分析.     

最优再保险及投资组合策略问题北大核心

为规避风险的巨大波动,保险公司会将承保的理赔进行分保,即再保险.假定再保险公司采用方差保费准则从保险公司收取保费.应用扩散逼近模型,刻画了保险公司有再保险控制下的资本盈余.另外,保险公司的盈余允许投资到利率、股票等金融市场.通过控制再保险及投资组合策略,研究了最小破产概率.应用动态规划方法(Hamilton-Jacobi-Bellman方程),对最小破产概率、最优再保险及投资组合策略给出了明晰解答,并给出了数值直观分析.     

基于损失相依保费原则下的最优再保险-投资策略

本文研究了基于损失相依保费原则下的最优再保险投资问题。该保费原则是基于过去的损失和对未来损失的估计来动态地更新保费，是传统的期望值保费原则的一个拓展。我们假设保险公司的盈余过程遵循C-L(Cramér-Lundberg)模型的扩散近似，保险公司通过购买比例再保险或获得新业务来分散风险或增加收益。假设金融市场由一个无风险资产和一个风险资产组成，其中风险资产的价格过程由仿射平方根随机模型描述。我们以最大化保险公司的终端时刻财富的期望效用为目标，利用动态规划，随机控制等方法得到CARA效用函数下的值函数的解析解，并得到最优再保险和投资策略的显性表达式。最后通过数值算例，分析了部分模型参数对最优再保险投资策略的影响。     

Exponential independence

For a set $S$ of vertices of a graph $G$, a vertex $u$ in $V\left(G\right)?S$, and a vertex $v$ in $S$, let ${\mathrm{dist}}_{(G,S)}(u,v)$ be the distance of $u$ and $v$ in the graph $G?(S?\left\{v\right\})$. Dankelmann et al. (2009) define $S$ to be an exponential dominating set of $G$ if $w_{(G,S)}\left(u\right)\ge 1$ for every vertex $u$ in $V\left(G\right)?S$, where $w_{(G,S)}\left(u\right)={\sum }_{v\in S}{\left(\frac{1}{2}\right)}^{{\mathrm{dist}}_{(G,S)}(u,v)?1}$. Inspired by this notion, we define $S$ to be an exponential independent set of $G$ if $w_{(G,S?\left\{u\right\})}\left(u\right)<1$ for every vertex $u$ in $S$, and the exponential independence number ${\alpha }_e\left(G\right)$ of $G$ as the maximum order of an exponential independent set of $G$.Similarly as for exponential domination, the non-local nature of exponential independence leads to many interesting effects and challenges. Our results comprise exact values for special graphs as well as tight bounds and the corresponding extremal graphs. Furthermore, we characterize all graphs $G$ for which ${\alpha }_e\left(H\right)$ equals the independence number $\alpha \left(H\right)$ for every induced subgraph $H$ of $G$, and we give an explicit characterization of all trees $T$ with ${\alpha }_e\left(T\right)=\alpha \left(T\right)$.     

Algebraic conditions on non-stationary subdivision symbols for exponential polynomial reproduction

We present an accurate investigation of the algebraic conditions that the symbols of a non-singular, univariate, binary, non-stationary subdivision scheme should fulfill in order to reproduce spaces of exponential polynomials. A subdivision scheme is said to possess the property of reproducing exponential polynomials if, for any initial data uniformly sampled from some exponential polynomial function, the scheme yields the same function in the limit. The importance of this property is due to the fact that several curves obtained by combinations of exponential polynomials (such as conic sections, spirals or special trigonometric and hyperbolic functions) are considered of interest in geometric modeling. Since the space of exponential polynomials trivially includes standard polynomials, this work extends the theory on polynomial reproduction to the non-stationary context. A significant application of the derived algebraic conditions on the subdivision symbols is the construction of new non-stationary subdivision schemes with specific reproduction properties.     

On the exponential sum—product problem

Let g be an element of order T over a finite field Fp of p elements, where p is a prime. We show that for a very wide class of sets A, B ∈ {1, . . . , T} at least one of the sets

{gab:a∈A,b∈B}and{ga+gb:a∈A,b∈B}     

An improved Mordell type bound for exponential sums

For a sparse polynomial , with and , we show that

thus improving upon a bound of Mordell. Analogous results are obtained for Laurent polynomials and for mixed exponential sums.

     

Approximation of exponential sums by shorter ones

A new theorem on approximation of exponential sum by shorter one is proved.     

On upper bounds of Chalk and Hua for exponential sums

Let be a polynomial of degree with integer coefficients, any prime, any positive integer and the exponential sum . We establish that if is nonconstant when read , then . Let , let be a zero of the congruence of multiplicity and let be the sum with restricted to values congruent to . We obtain for odd, and . If, in addition, , then we obtain the sharp upper bound .

     

Exponential Rosenbrock integrators for option pricing

In this paper, we are concerned with the time integration of differential equations modeling option pricing. In particular, we consider the Black-Scholes equation for American options. As an alternative to existing methods, we present exponential Rosenbrock integrators. These integrators require the evaluation of the exponential and related functions of the Jacobian matrix. The resulting methods have good stability properties. They are fully explicit and do not require the numerical solution of linear systems, in contrast to standard integrators. We have implemented some numerical experiments in Matlab showing the reliability of the new method.     

On the ratio of values of a polynomial

For given positive integersa andb, the equationa(x + 1)… (x + k) =b(y+1)… (y + k) in positive integers is considered. More general equations are also considered.