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1.
关于双曲衰减的违约相关模型及CDS定价   总被引:3,自引:0,他引:3  
引进一个双曲类型的衰减函数来表示一方违约对另一方违约强度的影响.若交易双方为竞争对手(合作公司),当一方的违约时,另一方的违约强度将减小(增大).随着时间的推移,这种影响将逐渐减小,直至为零.在这个模型下,通过测度变换,可以得到两公司违约时间的联合分布及各自的边际分布,从而可以对违约互换进行定价.  相似文献
2.
"边信息"的效用优化及其影响   总被引:1,自引:0,他引:1  
本文考虑受随机因素影响的股票价模型 ,投资者仅知道的股价信息 (公共信息 )和“边信息”的效用优化问题 .我们利用测度的变换和投影 ,给出了具有“边信息”和不具“边信息”两种情况下的最优财富形式 .对于对数效用函数 ,我们比较最优效用 ,讨论了“边信息”的影响  相似文献
3.
Some Results behind Dividend Problems   总被引:1,自引:0,他引:1  
We consider the basic dividend problem of the compound Poisson model with constant barrierstrategy.Some results concealed behind the dividend problem are made explicit in the present work.Differentmethods and some of which are firstly given in this paper.All these results presented certain direct relationshipbetween some important actuary variables in classical risk theory is also revealed.  相似文献
4.
随机利率下奇异期权的定价公式   总被引:1,自引:0,他引:1       下载免费PDF全文
李淑锦  李胜宏 《数学学报》2008,51(2):299-310
在随机利率条件下,借助于测度变换获得了复合看涨期权的一般的定价公式,同时利用鞅理论和Girsanov定理,在利率服从于扩展的Vasicek利率模型时,得到了复合看涨期权精确的定价公式.用同样的方法,考虑了预设日期的重置看涨期权的定价问题,在利率服从同样的利率模型时,获得了重置看涨期权的定价公式.数值化的结果进一步说明了当利率遵循扩展的Vasicek利率模型时,B-S看涨期权的价格关于标的资产的价格是严格单调递增的,复合看涨期权的Geske公式是可以推广到随机利率的情况.  相似文献
5.
Søren Asmussen 《Extremes》1998,1(2):137-168
The present state of extreme value theory for queues is surveyed. The exposition focuses on the regenerative properties of queueing systems, which reduces the problem to the study of the tail of the maximum of the queueing process during a regenerative cycle . For simple queues, methods for obtaining the distribution of both explicitly and asymptotically are reviewed. In greater generality, the study leads into Wiener–Hopf problems. Extensions to queues in a Markov regime, for example governed by Markov-modulated Poisson arrivals, are also considered.  相似文献
6.
The continuity conditions at the endpoints of interpolation theorems, TaBjMj aAj for j=0, 1, can be written with the help of the approximation functional: E(tTaB1B0)LM0 aA0 and E(tTaB0B1)LM1 aA1. As a special case of the results we present here we show that in the hypotheses of the interpolation theorem the L norms can be replaced by BMO( +) norms. This leads to a strong version of the Stein-Weiss theorem on interpolation with change of measure. Another application of our results is that the condition fL0, i.e., f*L, where f*(γ)=μ{|f|>γ} is the distribution function of f, can be replaced in interpolation with L(pq) spaces by the weaker f*BMO( +).  相似文献
7.
We study the asymptotic tail behavior of the maximum M = max{0,S n ,n ≥ = 1} of partial sums S n = ξ1 + ⋯ + ξ n of independent identically distributed random variables ξ12,... with negative mean. We consider the so-called Cramer case when there exists a β > 0 such that E e βξ1 = 1. The celebrated Cramer-Lundberg approximation states the exponential decay of the large deviation probabilities of M provided that Eξ1 e βξ1 is finite. In the present article we basically study the critical case Eξ1 e βξ1 = ∞. Original Russian Text Copyright ? 2005 Korshunov D. A. The author was supported by the Russian Foundation for Basic Research (Grant 05-01-00810) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-2139.2003.1). __________ Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 1335–1340, November–December, 2005.  相似文献
8.
This paper presents a large deviation analysis of the steady-state sojourn time distribution in the GI/G/1 PS queue. Logarithmic estimates are obtained under the assumption of the service time distribution having a light tail, thus supplementing recent results for the heavy-tailed setting. Our proof gives insight into the way a large sojourn time occurs, enabling the construction of an (asymptotically efficient) importance sampling algorithm. Finally our results for PS are compared to a number of other service disciplines, such as FCFS, LCFS, and SRPT. 2000 mathematics subject classification: 60K25.  相似文献
9.
In this paper, we identify the local rate function governing the sample path large deviation principle for a rescaled process n –1 Q nt , where Q t represents the joint number of clients at time t in a polling system with N nodes, one server and Markovian routing. By the way, the large deviation principle is proved and the rate function is shown to have the form conjectured by Dupuis and Ellis. We introduce a so called empirical generator consisting of Q t and of two empirical measures associated with S t , the position of the server at time t. One of the main step is to derive large deviations bounds for a localized version of the empirical generator. The analysis relies on a suitable change of measure and on a representation of fluid limits for polling systems. Finally, the rate function is solution of a meaningful convex program. The method seems to have a wide range of application including the famous Jackson networks, as shown at the end of this study. An example illustrates how this technique can be used to estimate stationary probability decay rate.  相似文献
10.
Markov modulated fluid models are widely used in modelling communications and computer systems. In the AMS (Annick, Mitra, Sohndi) model, heterogeneous, bursty sources modeled by multidimensional Markov processes are superimposed or multiplexed together to drive a fluid buffer. The performance of the system is measured by the steady state probability that the buffer exceeds a high level. The exact solution to this problem derived by AMS requires too much computation to be used on-line. Here we derive an upper bound for the above probability which is fast to compute and accurate enough for practical use.  相似文献
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