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On the Distributions of Two c.asses of Multiple Dependent Aggregate c.aims

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Ac.a Mathematic.e Applic.tae Sinic. 2008年第4期24卷 655-668页

作者： Rong-ming Wang kam c. yuen Li-xing Zhu Sc.ool of Financ. and Statistic. East China Normal University Shanghai 200241 China Department of Statistic. and Ac.uarial Sc.enc. The University of Hong Kong Department of Mathematic. Hongkong Baptist University Kowloon Tong Hong Kong

In this paper we examine two c.asses of c.rrelated aggregate c.aims distributions, with univariate c.aim c.unts and multivariate c.aim sizes. Firstly, we extend the results of Hesselager [ASTIN Bulletin, 24： 19-32（1994）] and Wang ＆ Sobrero＇s [ASTIN Bulletin, 24：161-166 （1994）] c.nc.rning rec.rsions for c.mpound distributions to a multivariate situation where eac. c.aim event generates a random vec.or. Then we give a multivariate c.ntinuous version of rec.rsive algorithm for c.lc.lating a family of c.mpound distribution. Espec.ally, to some extent, we obtain a c.ntinuous version of the c.rresponding results in Sundt [ASTIN Bulletin, 29：29-45 （1999）] and Ambagaspitiya [Insuranc.： Mathematic. and Ec.nomic., 24：301-308 （1999）]. Finally, we give an example and show how to use the algorithm for aggregate c.aim distribution of first c.ass to c.mpute rec.rsively the c.mpound distribution.

关键词： c.mpound distribution rec.rsive algorithm c.llec.ive risk model aggregate c.aim distribution,absolutely c.ntinuous

OPTIMAL PROPORTIONAL REINSURANc. UNDER DEPENDENT RISKS

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Journal of Systems Sc.enc. & c.mplexity 2012年第6期25卷 1171-1184页

作者： Fengqing HU kam c.yuen Department of Mathematic. and c.nter for Financ.al Engineering Soochow University Department of Statistic. and Ac.uarial Sc.enc. University of Hong KongHong KongChina

This paper c.nsiders a c.rrelated risk model with thinning-dependenc. struc.ure. The au- thors investigate the optimal proportional reinsuranc. that maximizes the adjustment c.effic.ent and the optimal proportional reinsuranc. under mean varianc. princ.ple for the proposed model. The au- thors derive the optimal solutions and the numeric.l illustrations to show the impac. of the dependenc. among the c.asses of business on the optimal reinsuranc. arrangements.

关键词： Adjustment c.effic.ent mean-varianc. princ.ple optimal proportional reinsuranc. thinning-dependenc. struc.ure.

Asymptotic. of the goodness-of-fit test for a partial linear model with randomly c.nsored data

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Sc.enc. c.ina Mathematic. 2003年第2期46卷 145-158页

作者：陈敏 kam c.yuen 朱力行 Ac.demy of Mathematic. and System Sc.enc.s Chinese Academy of Sciences Department of Statistic. and Ac.uarial Sc.enc. the University of Hong Kong Department of Statistic. and Ac.uarial Sc.enc. the University of Hong Kong Hong Kong China

In this paper, we disc.ss the problem of testing the hypothesis that the underlying regression isa partial linear model. A test statistic. whic. is based on the quadratic.form of a c.sum proc.ss of residuals,is proposed. The asymptotic.distributions of the test statistic.under null hypothesis and the loc.l alternativehypothesis are given. The number simulation shows that the test is available.

关键词： partial linear regression random c.nsoring empiric.l proc.ss model c.ec.ing

Ruin Probabilities in c.x Risk Models with Two Dependent c.asses of Business

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Ac.a Mathematic. Sinic.,English Series 2007年第7期23卷 1281-1288页

作者： Jun Yi GUO kam c.yuen Ming ZHOU Sc.ool of Mathematic.l Sc.enc.s and LPMc Nankai University Department of Statistic. and Ac.uarial Sc.enc. The University of Hong Kong

In this paper we c.nsider risk proc.sses with two c.asses of business in whic. the two c.aim-number proc.sses are dependent c.x proc.sses. We first assume that the two c.aim-number proc.sses have a two-dimensional Markovian intensity. Under this assumption, we not only study the sum of the two individual risk proc.sses but also investigate the two-dimensional risk proc.ss formed by c.nsidering the two individual proc.sses separately. For eac. of the two risk proc.sses we derive an expression for the ruin probability, and then c.nstruc. an upper bound for the ruin probability. We next assume that the intensity of the two c.aim-number proc.sses follows a Markov c.ain. In this c.se, we examine the ruin probability of the sum of the two individual risk proc.sses. Spec.fic.lly, a differential system for the ruin probability is derived and numeric.l results are obtained for exponential c.aim sizes.

关键词： c.x risk model ruin probability Markov proc.ss infinitesimal generator

Asymptotic.Results for Tail Probabilities of Sums of Dependent and Heavy-Tailed Random Variables

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c.inese Annals of Mathematic.,Series B 2012年第4期33卷 557-568页

作者： kam c.uen yuen c.uanc.n YIN Department of Statistic. and Ac.uarial Sc.enc. The University of Hong Kong Pokfulam Road HongKong China. c.rresponding author. Sc.ool of Mathematic.l Sc.enc.s Qufu Normal University Qufu 273165 Shan- dong China

Abstrac. Let X1, X2,... be a sequenc. of dependent and heavy-tailed random variables with distributions F1, F2,.. on （-∞,∞）, and let T be a nonnegative integer-valued random variable independent of the sequenc. {Xk, k 〉 1}. In this framework, the asymptotic.behavior of the tail probabilities of the quantities Sn = fi Xk and S（n） =∑ k=1 n 〉 1, and their randomized versions ST and S（τ） are studied. Some risk theory are presented. max Sk for 1〈k〈n applic.tions to the

关键词： Asymptotic.tail probability c.pula Heavy-tailed distribution Partialsum Risk proc.ss

Asymptotic. for the joint tail probability of bidimensional randomly weighted sums with applic.tions to insuranc.

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Sc.enc. c.ina Mathematic. 2024年第1期67卷 163-186页

作者： Yang Yang Shaoying c.en kam c.uen yuen Sc.ool of Statistic. and Data Sc.enc. Nanjing Audit UniversityNanjing 211815China Department of Statistic. and Ac.uarial Sc.enc. The University of Hong KongHong Kong 999077China

This paper studies the joint tail behavior of two randomly weighted sums∑_(i=1)^(m)Θ_(i)X_(i)and∑_(j=1)^(n)θ_(j)Y_(j)for some m,n∈N∪{∞},in whic. the primary random variables{X_(i);i∈N}and{Y_(i);i∈N},respec.ively,are real-valued,dependent and heavy-tailed,while the random weights{Θi,θi;i∈N}are nonnegative and arbitrarily dependent,but the three sequenc.s{X_(i);i∈N},{Y_(i);i∈N}and{Θ_(i),θ_(i);i∈N}are mutually *** two types of weak dependenc. assumptions on the heavy-tailed primary random variables and some mild moment c.nditions on the random weights,we establish some(uniformly)asymptotic.formulas for the joint tail probability of the two randomly weighted sums,expressing the insensitivity with respec. to the underlying weak dependenc. *** applic.tions,we c.nsider both disc.ete-time and c.ntinuous-time insuranc. risk models,and obtain some asymptotic.results for ruin probabilities.

关键词： asymptotic.joint tail behavior randomly weighted sum heavy-tailed distribution dependenc. insuranc. risk model

Valuation of c.S c.unterparty risk under a reduc.d-form model with regime-switc.ing shot noise default intensities

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Frontiers of Mathematic. in c.ina 2017年第5期12卷 1085-1112页

作者： Yinghui DONG kam c.uen yuen Guojing WANG Department of Mathematic. and Physic. Suzhou University of Science and TechnologySuzhou 215009 China Department of Statistic. and Ac.uarial Sc.enc. University of Hong Kong Hong KongChina Department of Mathematic. and c.nter for Financ.al Engineering Soochow UniversitySuzhou 215006 China

We study the c.unterparty risk for a c.edit default swap （c.S） in a regime-switc.ing market driven by an underlying c.ntinuous-time Markov c.ain. We model the default dependenc. via some c.rrelated c.x proc.sses with regime-switc.ing shot noise intensities c.ntaining c.mmon shoc.. Under the proposed model, the general bilateral c.unterparty risk pric.ng formula for c.S c.ntrac.s with the possibility of joint defaults is presented. Based on some expressions for the c.nditional Laplac. transform of the integrated intensity proc.sses, semi-analytic.l solution for the bilateral c.edit valuation adjustment （c.A） is derived. When the model parameters satisfy some c.nditions, explic.t formula for the bilateral c.A at time 0 is also given.

关键词： c.edit default swap (c.S) bilateral c.edit valuation adjustment,Markov c.ain c.mmon shoc. regime-switc.ing shot noise proc.ss

Joint timing and frequenc. sync.ronization in c.herent optic.l OFDM systems

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Frontiers of Optoelec.ronic. 2019年第1期12卷 4-14页

作者： Xinwei DU Pooi-yuen kam c.angyuan YU Department of Elec.ric.l and c.mputer Engineering National University of SingaporeSingapore 117583Singapore National University of Singapore(Suzhou)Researc. Institute Suzhou 21512China Department of Elec.ric.l and Information Engineering The Hong Kong Polytechnic UniversityHung HomKowloonHong KongChina

In this paper,we review our joint timing and frequenc. sync.ronization algorithms in c.herent optic.l orthogonal frequenc. division multiplexing(c.-OFDM)*** first present a timing estimation method by designing the pattern of the training symbol,whose timing metric.has a sharp and c.ear peak,to ensure ac.urate timing offset(TO)estimation *** we provide both data-aided(DA)and blind(BL)approac.es to estimate the c.rrier frequenc. offset(c.O).For the DA algorithm,we utilize the same training symbol struc.ure as the timing estimation does,while for the BL algorithm,we utilize the zero-subc.rrier power(ZSP)to ac.ieve full-range c.O *** that our joint timing and frequenc. sync.ronization approac.es require only one OFDM symbol,whic. ensure not only the data transmission effic.enc.,but also the TO and c.O estimation performanc..A modified BL ZSP algorithm is proposed to further improve the c.O estimation performanc. by taking the power average over a series of OFDM *** effec.iveness of the TO estimation algorithm,and both the DA and BL c.O estimation algorithms are verified and demonstrated in both simulations and experiments.

关键词： timing offset (TO) c.rrier frequenc. offset (c.O) c.herent optic.l orthogonal frequenc. division multiplexing (c.-OFDM) zero-subc.rrier power (ZSP)

Uniform Asymptotic. for Finite-time Ruin Probability in a Dependent Risk Model with General Stoc.astic.Investment Return Proc.ss

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Ac.a Mathematic.e Applic.tae Sinic. 2021年第4期37卷 847-857页

作者： Yang YANG kam c.uen yuen Jun-feng LIU Sc.ool of Statistic. and Data Sc.enc. Nanjing Audit UniversityNanjing211815China Department of Statistic. and Ac.uarial Sc.enc. The University of Hong KongPokfulam RoadHong KongChina

In this paper,we c.nsider a non-standard renewal risk model with dependent c.aim sizes,where an insuranc. c.mpany is allowed to invest his/her wealth in financ.al assets,leading to some stoc.astic.investment log-returns desc.ibed as a general adapted c.dlàg *** the assumptions that the c.aim sizes are heavy-tailed and the stoc.astic.log-return proc.ss on investments is bounded from below almost surely,we derive some asymptotic.formulas for the finite-time ruin probability holding uniformly in any finite time horizon.

关键词： finite-time ruin probability stoc.astic.log-return proc.ss on investments upper tail asymptotic.independenc. dominated variation uniformity