共查询到20条相似文献,搜索用时 15 毫秒
1.
Simard Clarence Rémillard Bruno 《Methodology and Computing in Applied Probability》2019,21(3):985-1005
In this paper we build a discrete time model for the structure of the limit order book, so that the price per share depends on the size of the transaction. We deduce the value of a portfolio when the investor trades using market orders and a bank account with different interest rates for lending and borrowing. We also deduce conditions to rule out arbitrage and solve the problem of pricing and hedging an European call option with physical delivery. It is shown that contrary to the perfectly liquid setting, the price of a European call is not given by an expectation, but can be expressed as an optimization problem on a set of equivalent probability measures.
相似文献2.
We consider two types of queues with workload-dependent arrival rate and service speed. Our study is motivated by queueing scenarios where the arrival rate and/or speed of the server depends on the amount of work present, like production systems and the Internet. First, in the M/G/1 case, we compare the steady-state distribution of the workload (both at arbitrary epochs and at arrival instants) in two models, in which the ratio of arrival rate and service speed is equal. Applying level crossing arguments, we show that the steady-state distributions are proportional. Second, we consider a G/G/1-type queue with workload-dependent interarrival times and service speed. Using a stochastic mean-value approach, several well-known relations for the workload at various epochs in the ordinary G/G/1 queue are generalized. 相似文献
3.
A weak dependence condition is derived as the natural generalization to random fields on notions developed in Doukhan and
Louhichi (1999). Examples of such weakly dependent fields are defined. In the context of a weak dependence coefficient series
with arithmetic or geometric decay, we give explicit bounds in Prohorov metric for the convergence in the empirical central
limit theorem. For random fields indexed by &Zopf
d
, in the geometric decay case, rates have the form n
−1/(8d+24)
L(n), where L(n) is a power of log(n).
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
4.
考虑一类具有相依结构的离散时间风险过程,其中利率和保费收入过程为两个不同的自回归移动平均模型.利用更新递归方法,得到了破产前盈余与破产后赤字的联合分布和破产持续时间分布的递归计算公式. 相似文献
5.
René Bekker 《Queueing Systems》2005,50(2-3):231-253
We consider M/G/1 queues with workload-dependent arrival rate, service speed, and restricted accessibility. The admittance of customers typically depends on the amount of work found upon arrival in addition to its own service requirement. Typical examples are the finite dam, systems with customer impatience and queues regulated by the complete rejection discipline. Our study is motivated by queueing scenarios where the arrival rate and/or speed of the server depends on the amount of work present, like production systems and the Internet.First, we compare the steady-state distribution of the workload in two finite-buffer models, in which the ratio of arrival and service speed is equal. Second, we find an explicit expression for the cycle maximum in an M/G/1 queue with workload-dependent arrival and service rate. And third, we derive a formal solution for the steady-state workload density in case of restricted accessibility. The proportionality relation between some finite and infinite-buffer queues is extended. Level crossings and Volterra integral equations play a key role in our approach.AMS subject classification: 60K25, 90B22 相似文献
6.
F. S. Chong 《Mathematische Nachrichten》1981,103(1):155-163
The limiting behaviour of the point process with 2nd order MARKOV-dependent intervals is analysed through the use of “regeneration time”. The results for the case of periodic MARKOV-dependent intervals are briefly mentioned. 相似文献
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10.
Birkel T. 《Journal of multivariate analysis》1993,44(2)
In this note we prove a functional central limit theorem for LPQD processes, satisfying some assumptions on the covariances and the moment condition supj≥1E|Xj|2+ρ < ∞ for some ρ > 0. 相似文献
11.
12.
Consider a system where units having random magnitude enter according to a Poisson process. While in the system, a unit's magnitude may change with time. In this paper we obtain a functional limit theorem for the sum process of all unit magnitudes present in the system at time t. 相似文献
13.
We propose a simple way, called the arrival time approach, of finding the queue length distributions for M/G/1-type queues with generalized server vacations. The proposed approach serves as a useful alternative to understanding complicated queueing processes such as priority queues with server vacations and MAP/G/1 queues with server vacations. 相似文献
14.
A Functional Central Limit Theorem for Asymptotically Negatively Dependent Random Fields 总被引:12,自引:0,他引:12
L.-X. Zhang 《Acta Mathematica Hungarica》2000,86(3):237-259
Let X
k
; k N
d
be a random field which is asymptotically negative dependent in a certain sense. Define the partial sum process in the usual way so that
, where
. Under some suitable conditions, we show that W
n
(·) converges in distribution to a Brownian sheet. Direct consequences of the result are functional central limit theorems for negative dependent random fields. The result is based on some general theorems concerning asymptotically negative dependent random fields, which are of independent interest. 相似文献
15.
Let be independent and identically distributed random variables with heavy-tailed distributions. Consider a sequence of random
weights , independent of and focus on the weighted sums , where μ involves a suitable centering. We establish sufficient conditions for these weighted sums to converge to non-trivial limit
processes, as n→∞, when appropriately normalized. The convergence holds, for example, if is strictly stationary, dependent, and W
1 has lighter tails than U
1. In particular, the weights W
j
s can be strongly dependent. The limit processes are scale mixtures of stable Lévy motions. We establish weak convergence
in the Skorohod J
1-topology. We also consider multivariate weights and show that they converge weakly in the strong Skorohod M
1-topology. The M
1-topology, while weaker than the J
1-topology, is strong enough for the supremum and infimum functionals to be continuous.
This research was partially supported by a fellowship of the Horace H. Rackham School of Graduate Studies at the University
of Michigan and the NSF Grants BCS-0318209 and DMS-0505747 at Boston University. 相似文献
16.
本文研究批量到达带启动时间的单重休假的M/G/1排队系统,给出稳态队长的母函数和等待时间分布的LST及其它们的随机分解结果,推导出忙期、闲期和线期母函数和均值。 相似文献
17.
具有不同到达率的带有启动时间及不耐烦策略的多级适应性休假M/G/1排队 总被引:1,自引:0,他引:1
研究了具有不同到达率的带有启动时间及不耐烦策略的多级适应性休假M/G/1排队模型,给出了稳态队长的母函数,等待时间的LST及其随机分解结果,并推导出忙期、全忙期及在线期均值. 相似文献
18.
19.
We consider the M(t)/M(t)/m/m queue, where the arrival rate λ(t) and service rate μ(t) are arbitrary (smooth) functions of time. Letting pn(t) be the probability that n servers are occupied at time t (0≤ n≤ m, t > 0), we study this distribution asymptotically, for m→∞ with a comparably large arrival rate λ(t) = O(m) (with μ(t) = O(1)). We use singular perturbation techniques to solve the forward equation for pn(t) asymptotically. Particular attention is paid to computing the mean number of occupied servers and the blocking probability
pm(t). The analysis involves several different space-time ranges, as well as different initial conditions (we assume that at t = 0 exactly n0 servers are occupied, 0≤ n0≤ m). Numerical studies back up the asymptotic analysis.
AMS subject classification: 60K25,34E10
Supported in part by NSF grants DMS-99-71656 and DMS-02-02815 相似文献