In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order ...In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.展开更多
In this paper,we establish a second-order necessary conditions for stochastic optimal control for jump diffusions.The controlled system is described by a stochastic differential systems driven by Poisson random measur...In this paper,we establish a second-order necessary conditions for stochastic optimal control for jump diffusions.The controlled system is described by a stochastic differential systems driven by Poisson random measure and an independent Brownian motion.The control domain is assumed to be convex.Pointwise second-order maximum principle for controlled jump diffusion in terms of the martingale with respect to the time variable is proved.The proof of the main result is based on variational approach using the stochastic calculus of jump diffusions and some estimates on the state processes.展开更多
In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-...In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-order asymptotics of the spectral risk measure of portfolio loss is also presented.In order to illustrate the derived results,a numerical example with Monte Carlo simulation is carried out.展开更多
Let {（ξni, ηni）, 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as （S1,ρnS1 ＋ √1- ρ2nS2）, ρn ∈（0, 1）, where （S1,S2） is...Let {（ξni, ηni）, 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as （S1,ρnS1 ＋ √1- ρ2nS2）, ρn ∈（0, 1）, where （S1,S2） is a bivariate spherical random vector. For the distribution function of radius√S12 ＋ S22 belonging to the max-domain of attraction of the Weibull distribution, the limiting distribution of maximum of this triangular array is known as the convergence rate of p~ to 1 is given. In this paper, under the refinement of the rate of convergence of p~ to 1 and the second-order regular variation of the distributional tail of radius, precise second-order distributional expansions of the normalized maxima of bivariate elliptical triangular arrays are established.展开更多
We study the conditional limit theorems for critical continuous-state branching processes with branching mechanism Ф（λ） = λ 1＋αL（1/λ）, where （α∈ [0, 1] and L is slowly varying at co. We prove that if α ...We study the conditional limit theorems for critical continuous-state branching processes with branching mechanism Ф（λ） = λ 1＋αL（1/λ）, where （α∈ [0, 1] and L is slowly varying at co. We prove that if α ∈ （0, 1], there are norming constants Qt →0 （as t ↑ ＋ ∞） such that for every x 〉 0, Px（QtXt ∈ · ｜Xt 〉 0） converges weakly to a non-degenerate limit. The converse assertion is also true provided the regularity of ψ at 0. We give a conditional limit theorem for the case α = 0. The limit theorems we obtain in this paper allow infinite variance of the branching process.展开更多
In this paper, based on the second-order sufficient condition, the Clarke's generalized Jacobian of the Karush-Kuhn-Tucker system of the second-order cone constrained variational inequality (SOCCVI) problem that i...In this paper, based on the second-order sufficient condition, the Clarke's generalized Jacobian of the Karush-Kuhn-Tucker system of the second-order cone constrained variational inequality (SOCCVI) problem that is nonsingular is proved by us. A modified Newton method with Armijo line search is presented. Three illustrative examples are given to show how the modified Newton method works.展开更多
We derive higher-order expansions of L-statistics of independent risks X1,..., Xn under conditions on the underlying distribution function F. The new results are applied to derive the asymptotic expansions of ratios o...We derive higher-order expansions of L-statistics of independent risks X1,..., Xn under conditions on the underlying distribution function F. The new results are applied to derive the asymptotic expansions of ratios of two kinds of risk measures, stop-loss premium and excess return on capital, respectively. Several examples and a Monte Carlo simulation study show the efficiency of our novel asymptotic expansions. Keywords smoothly varying condition, second-order regular variation, tail asymptotics, value-at-risk, con- ditional tail expectation, largest claims reinsurance, ratio of risk measure, excess return on capital展开更多
文摘In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.
文摘In this paper,we establish a second-order necessary conditions for stochastic optimal control for jump diffusions.The controlled system is described by a stochastic differential systems driven by Poisson random measure and an independent Brownian motion.The control domain is assumed to be convex.Pointwise second-order maximum principle for controlled jump diffusion in terms of the martingale with respect to the time variable is proved.The proof of the main result is based on variational approach using the stochastic calculus of jump diffusions and some estimates on the state processes.
基金supported by the Important Natural Science Foundation of Colleges and Universities of Anhui Province under Grant No.KJ2020A0122the Scientific Research Start-up Foundation of Hefei Normal University。
文摘In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-order asymptotics of the spectral risk measure of portfolio loss is also presented.In order to illustrate the derived results,a numerical example with Monte Carlo simulation is carried out.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11501113,11601330 and 11701469)the Key Project of Fujian Education Committee(Grant No.JA15045)the Funding Program for Junior Faculties of College and Universities of Shanghai Education Committee(Grant No.ZZslg16020)
文摘Let {（ξni, ηni）, 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as （S1,ρnS1 ＋ √1- ρ2nS2）, ρn ∈（0, 1）, where （S1,S2） is a bivariate spherical random vector. For the distribution function of radius√S12 ＋ S22 belonging to the max-domain of attraction of the Weibull distribution, the limiting distribution of maximum of this triangular array is known as the convergence rate of p~ to 1 is given. In this paper, under the refinement of the rate of convergence of p~ to 1 and the second-order regular variation of the distributional tail of radius, precise second-order distributional expansions of the normalized maxima of bivariate elliptical triangular arrays are established.
基金The National Natural Science Foundation of China(61379019)the Fundamental Research Funds for the Central Universities,Southwest University for Nationalities(2014NZYQN29)
基金supported by National Natural Science Foundation of China(Grant Nos.11271030 and 11128101)Specialized Research Fund for the Doctoral Program of Higher Education and China Postdoctoral Science Foundation(Grant No.2013M541061)
文摘We study the conditional limit theorems for critical continuous-state branching processes with branching mechanism Ф（λ） = λ 1＋αL（1/λ）, where （α∈ [0, 1] and L is slowly varying at co. We prove that if α ∈ （0, 1], there are norming constants Qt →0 （as t ↑ ＋ ∞） such that for every x 〉 0, Px（QtXt ∈ · ｜Xt 〉 0） converges weakly to a non-degenerate limit. The converse assertion is also true provided the regularity of ψ at 0. We give a conditional limit theorem for the case α = 0. The limit theorems we obtain in this paper allow infinite variance of the branching process.
文摘In this paper, based on the second-order sufficient condition, the Clarke's generalized Jacobian of the Karush-Kuhn-Tucker system of the second-order cone constrained variational inequality (SOCCVI) problem that is nonsingular is proved by us. A modified Newton method with Armijo line search is presented. Three illustrative examples are given to show how the modified Newton method works.
基金supported by the Swiss National Science Foundation(Grant Nos.2000211401633/1,200021-134785 and 200021-1401633/1)Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme(Grant No.RARE-318984)+1 种基金National Natural Science Foundation of China(Grant No.11171275)the Natural Science Foundation Project of Chongqing(Grant No.cstc2012jjA00029)
文摘We derive higher-order expansions of L-statistics of independent risks X1,..., Xn under conditions on the underlying distribution function F. The new results are applied to derive the asymptotic expansions of ratios of two kinds of risk measures, stop-loss premium and excess return on capital, respectively. Several examples and a Monte Carlo simulation study show the efficiency of our novel asymptotic expansions. Keywords smoothly varying condition, second-order regular variation, tail asymptotics, value-at-risk, con- ditional tail expectation, largest claims reinsurance, ratio of risk measure, excess return on capital
