http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2010/875908.htmlSo far there are not many results on the stability for stochastic functional differential equations with infinite delay. The main aim of this paper is to establish some new criteria on the stability with general decay rate for stochastic functional differential equations with infinite delay. To illustrate the applications of our theories clearly, this paper also examines a scalar infinite delay stochastic functional differential equations with polynomial coefficients.Yue Liu, Xuejing Meng, and Fuke Wu© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2009/782572.htmlThis paper considers the pricing of a European option using a (B,S)-market in which the stock price and the asset in the riskless bank account both have hereditary price structures described by the authors of this paper (1999). Under the smoothness assumption of the payoff function, it is shown that the infinite dimensional Black-Scholes equation possesses a unique classical solution. A spectral approximation scheme is developed using the Fourier series expansion in the space C[−h,0] for the Black-Scholes equation. It is also shown that the nth approximant resembles the classical Black-Scholes equation in finite dimensions.Mou-Hsiung Chang and Roger K. Youree© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2009/975601.htmlWe study a boundary value problem with multivariables integral type condition for a class of parabolic equations. We prove the existence, uniqueness, and continuous dependence of the solution upon the data in the functional wieghted Sobolev spaces. Results are obtained by using a functional analysis method based on two-sided a priori estimates and on the density of the range of the linear operator generated by the considered problem.A. L. Marhoune and F. Lakhal© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2009/215817.htmlWe investigate the arbitrage-free property of stock price models where the local martingale component is based on an ergodic diffusion with a specified stationary distribution. These models are particularly useful for long horizon asset-liability management as they allow the modelling of long term stock returns with heavy tail ergodic diffusions, with tractable, time homogeneous dynamics, and which moreover admit a complete financial market, leading to unique pricing and hedging strategies. Unfortunately the standard specifications of these models in literature admit arbitrage opportunities. We investigate in detail the features of the existing model specifications which create these arbitrage opportunities and consequently construct a modification that is arbitrage free.Bernard Wong© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2009/695798.htmlThe valuation and hedging of defaultable game options is studied in a hazard process model of credit risk. A convenient pricing formula with respect to a reference filteration is derived. A connection of arbitrage prices with a suitable notion of hedging is obtained. The main result shows that the arbitrage prices are the minimal superhedging prices with sigma martingale cost under a risk neutral measure.Tomasz R. Bielecki, Stéphane Crépey, Monique Jeanblanc, and Marek Rutkowski© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2009/308025.htmlWe consider the interloss times in the M/M/1/1 Erlang Loss System. Here we present the explicit form of the probability density function of the time spent between two consecutive losses in the M/M/1/1 model. This density function solves a Cauchy problem for the second-order differential equations, which was used to evaluate the corresponding laplace transform. Finally the connection between the Erlang's loss rate and the evaluated probability density function is showed.Pierpaolo Ferrante© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2009/854768.htmlWe study a new type of reflected backward stochastic differential equations (RBSDEs), where the reflecting process enters the drift in a nonlinear manner. This type of the reflected BSDEs is based on a variance of the Skorohod problem studied recently by Bank and El Karoui (2004), and is hence named the “Variant Reflected BSDEs” (VRBSDE) in this paper. The special nature of the Variant Skorohod problem leads to a hidden forward-backward feature of the BSDE, and as a consequence this type of BSDE cannot be treated in a usual way. We shall prove that in a small-time duration most of the well-posedness, comparison, and stability results are still valid, although some extra conditions on the boundary process are needed. We will also provide some possible applications where the VRBSDE can be potentially useful. These applications show that the VRBSDE could become a novel tool for some problems in finance and optimal stopping problems where no existing methods can be easily applicable.Jin Ma and Yusun Wang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2009/320820.htmlLet H be a real Hilbert space, let S, T be two nonexpansive mappings such that F(S)∩F(T)≠∅, let f be a contractive mapping, and let A be a strongly positive linear bounded operator on H. In this paper, we suggest and consider the strong converegence analysis of a new two-step iterative algorithms for finding the approximate solution of two nonexpansive mappings as xn+1=βnxn+(1−βn)Syn, yn=αnγf(xn)+(I−αnA)Txn, n≥0 is a real number and {αn}, {βn} are two sequences in (0,1) satisfying the following control conditions: (C1) lim⁡n→∞ αn=0, (C3) 0<lim⁡inf⁡n→∞ βn≤lim⁡sup⁡n→∞ βn<1, then ‖xn+1−xn‖→0. We also discuss several special cases of this iterative algorithm.Yonghong Yao, Muhammad Aslam Noor, and Syed Tauseef Mohyud-Din© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2009/725260.htmlThe expected number of real zeros of an algebraic polynomial ao+a1x+a2x2+⋯+anxn with random coefficient aj,j=0,1,2,…,n is known. The distribution of the coefficients is often assumed to be identical albeit allowed to have different classes of distributions. For the nonidentical case, there has been much interest where the variance of the jth coefficient is var ⁡(aj)=(nj). It is shown that this class of polynomials has significantly more zeros than the classical algebraic polynomials with identical coefficients. However, in the case of nonidentically distributed coefficients it is analytically necessary to assume that the means of coefficients are zero. In this work we study a case when the moments of the coefficients have both binomial and geometric progression elements. That is we assume E(aj)=(nj)μj+1 and var ⁡(aj)=(nj)σ2j. We show how the above expected number of real zeros is dependent on values of σ2 and μ in various cases.K. Farahmand and M. Sambandham© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2009/254720.htmlWe give a theorem on implicit difference functional inequalities generated by mixed problems for nonlinear systems of first-order partial differential functional equations. We apply this result in the investigations of the stability of difference methods. Classical solutions of mixed problems are approximated in the paper by solutions of suitable implicit difference schemes. The proof of the convergence of difference method is based on comparison technique, and the result on difference functional inequalities is used. Numerical examples are presented.Z. Kamont and K. Kropielnicka© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/104525.htmlThis study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.M. Ilić, I. W. Turner, and V. Anh© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/359142.htmlWe obtain a Hull and White type formula for a general jump-diffusion stochastic volatility model, where the involved stochastic volatility process is correlated not only with the Brownian motion driving the asset price but also with the asset price jumps. Towards this end, we establish an anticipative Itô's formula, using Malliavin calculus techniques for Lévy processes on the canonical space. As an application, we show that the dependence of the volatility process on the asset price jumps has no effect on the short-time behavior of the at-the-money implied volatility skew.Elisa Alòs, Jorge A. León, Monique Pontier, and Josep Vives© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/149483.htmlWe define a viscosity method for continuous pseudocontractive mappings defined on closed and convex subsets of reflexive Banach spaces with a uniformly Gâteaux differentiable norm. We prove the convergence of these schemes improving the main theorems in the work by Y. Yao et al. (2007) and H. Zhou (2008).Filomena Cianciaruso, Giuseppe Marino, Luigi Muglia, and Haiyun Zhou© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/905721.htmlWe analyze the survival time of a renewable duplex system characterized by warm standby and subjected to a priority rule. In order to obtain the Laplace transform of the survival function, we employ a stochastic process endowed with time-dependent transition measures satisfying coupled partial differential equations. The solution procedure is based on the theory of sectionally holomorphic functions combined with the notion of dual transforms. Finally, we introduce a security interval related to a prescribed security level and a suitable risk criterion based on the survival function of the system. As an example, we consider the particular case of deterministic repair. A computer-plotted graph displays the survival function together with the security interval corresponding to a security level of 90%.Edmond J. Vanderperre© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/396871.htmlWe consider a two-heterogeneous-server queueing system with Bernoulli vacation in which customers arrive according to a Markovian arrival process (MAP). Servers returning from vacation immediately take another vacation if no customer is waiting. Using matrix-geometric method, the steady-state probability of the number of customers in the system is investigated. Some important performance measures are obtained. The waiting time distribution and the mean waiting time are also discussed. Finally, some numerical illustrations are provided.B. Krishna Kumar, R. Rukmani, and V. Thangaraj© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/367170.htmlApplying piecewise deterministic Markov processes theory, the probability generating function of a Cox process, incorporating with shot noise process as the claim intensity, is obtained. We also derive the Laplace transform of the distribution of the shot noise process at claim jump times, using stationary assumption of the shot noise process at any times. Based on this Laplace transform and from the probability generating function of a Cox process with shot noise intensity, we obtain the distribution of the interval of a Cox process with shot noise intensity for insurance claims and its moments, that is, mean and variance.Angelos Dassios and Jiwook Jang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/821243.htmlWe consider the problem of risk indifference pricing on an incomplete market, namely on a jump diffusion market where the controller has limited access to market information. We use the maximum principle for stochastic differential games to derive a formula for the risk indifference price priskseller(G,ℰ) of a European-type claim G.Ta Thi Kieu An, Bernt Øksendal, and Frank Proske© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/130940.htmlThis article aims to give a formula for differentiating, with respect to T, an expression of the form λ(T,x):=𝔼x[f(XT)e−∫0TV(Xs)ds(det⁡(I+KX,T))P], where p≥0 and X is a diffusion process starting from x, taking values in a manifold, and the expectation is taken with respect to the law of this process. KX,T:L2([0,T)→ℝN)→L2([0,T)→ℝN) is a trace class operator defined by KX,Tf(s)=∫0TH(s∧t)Γ(X(t))f(t)dt, where H, Γ are locally Lipschitz, positive N×N matrices.Adrian P. C. Lim© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/473156.htmlThis paper considers necessary and sufficient conditions for the solution of a stochastically and deterministically perturbed Volterra equation to converge exponentially to a nonequilibrium and nontrivial limit. Convergence in an almost sure and pth mean sense is obtained.John A. D. Appleby, Siobhán Devin, and David W. Reynolds© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/564601.htmlLet Xt={X(t), t≥0} be a one-dimensional symmetric Cauchy process. We prove that, for any measure function, φ,φ−p(X[0,τ]) is zero or infinite, where φ−p(E) is the φ-packing measure of E, thus solving a problem posed by Rezakhanlou and Taylor in 1988.A. C. Okoroafor© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/158193.htmlThis paper revisits the classical discrete-time stationary inventory model. A new proof, based on the theory of quasivariational inequality (QVI), of the optimality of (s,S) policy is presented. This proof reveals a number of interesting properties of the optimal cost function. Further, the proof could be used as a tutorial for applications of QVI to inventory control.Lakdere Benkherouf© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/275217.htmlWe present an algorithm producing a dynamic non-self-financing hedging strategy in an incomplete market corresponding to investor-relevant risk criterion. The optimization is a two-stage process that first determines market calibrated model parameters that correspond to the market price of the option being hedged. In the second stage, an optimal set of model parameters is chosen from the market calibrated set. This choice is based on stock price simulations using a time-series model for stock price jump evolution. Results are presented for options traded on the New York Stock Exchange.N. Josephy, L. Kimball, and V. Steblovskaya© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/518214.htmlFluid queues offer a natural framework for analyzing waiting times in a relay node of an ad hoc network. Because of the resource sharing policy applied, the input and output of these queues are coupled. More specifically, when there are n users who wish to transmit data through a specific node, each of them obtains a share 1/(n+w) of the service capacity to feed traffic into the queue of the node, whereas the remaining fraction w/(n+w) is used to serve the queue; here w>0 is a free design parameter. Assume now that jobs arrive at the relay node according to a Poisson process, and that they bring along exponentially distributed amounts of data. The case w=1 has been addressed before; the present paper focuses on the intrinsically harder case w>1, that is, policies that give more weight to serving the queue. Four performance metrics are considered: (i) the stationary workload of the queue, (ii) the queueing delay, that is, the delay of a “packet” (a fluid particle) that arrives at an arbitrary point in time, (iii) the flow transfer delay, (iv) the sojourn time, that is, the flow transfer time increased by the time it takes before the last fluid particle of the flow is served. We explicitly compute the Laplace transforms of these random variables.Michel Mandjes and Werner Scheinhardt© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/474623.htmlWe propose a model for valuing participating life insurance products under a generalized jump-diffusion model with a Markov-switching compensator. It also nests a number of important and popular models in finance, including the classes of jump-diffusion models and Markovian regime-switching models. The Esscher transform is employed to determine an equivalent martingale measure. Simulation experiments are conducted to illustrate the practical implementation of the model and to highlight some features that can be obtained from our model.Tak Kuen Siu, John W. Lau, and Hailiang Yang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/189675.htmlThe expected number of real zeros of the polynomial of the form a0+a1x+a2x2+⋯+anxn, where a0,a1,a2,…,an is a sequence of standard Gaussian random variables, is known. For n large it is shown that this expected number in (−∞,∞) is asymptotic to (2/π)log⁡n. In this paper, we show that this asymptotic value increases significantly to n+1 when we consider a polynomial in the form a0(n0)1/2x/1+a1(n1)1/2x2/2+a2(n2)1/2x3/3+⋯+an(nn)1/2xn+1/n+1 instead. We give the motivation for our choice of polynomial and also obtain some other characteristics for the polynomial, such as the expected number of level crossings or maxima. We note, and present, a small modification to the definition of our polynomial which improves our result from the above asymptotic relation to the equality.K. Farahmand, A. Grigorash, and B. McGuinness© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/254897.htmlVarious upper bounds for the L2-norm of the Wick product of two measurable functions of a random variable X, having finite moments of any order, together with a universal minimal condition, are proven. The inequalities involve the second quantization operator of a constant times the identity operator. Some conditions ensuring that the constants involved in the second quantization operators are optimal, and interesting examples satisfying these conditions are also included.Alberto Lanconelli and Aurel I. Stan© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/735436.htmlLet F^n be an estimator obtained by integrating a kernel type density estimator based on a random sample of size n. A central limit theorem is established for the target statistic F^n(ξ^n), where the underlying random vector forms an asymptotically stationary absolutely regular stochastic process, and ξ^n is an estimator of a multivariate parameter ξ by using a vector of U-statistics. The results obtained extend or generalize previous results from the stationary univariate case to the asymptotically stationary multivariate case. An example of asymptotically stationary absolutely regular multivariate ARMA process and an example of a useful estimation of F(ξ) are given in the applications.Echarif Elharfaoui and Michel Harel© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/275747.htmlWe consider the martingale problem related to the solution of an SDE on the line. It is shown that the solution of this martingale problem can be approximated by solutions of the corresponding time-discrete martingale problems under some conditions. This criterion is especially expedient for establishing the convergence of population processes to SDEs. We also show that the criterion yields a weak Euler scheme approximation of SDEs under fairly weak assumptions on the driving force of the approximating processes.Henryk Zähle© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/160303.htmlWe introduce the fractional mixed fractional Brownian sheet and investigate the small ball behavior of its sup-norm statistic by establishing a general result on the small ball probability of the sum of two not necessarily independent joint Gaussian random vectors. Then, we state general conditions and characterize the sufficiency part of the lower classes of some statistics of the above process by an integral test. Finally, when we consider the sup-norm statistic, the necessity part is given by a second integral test.Charles El-Nouty© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2008/760214.htmlIn 1997, Haruki and Rassias introduced two generalizations of the Poisson kernel in two dimensions and discussed integral formulas for them. Furthermore, they presented an open problem. In 1999, Kim gave a solution to that problem. Here, we give a solution to this open problem by means of a different method. The purpose of this paper is to give integral averages of two generalizations of the Poisson kernel, that is, we generalize the open problem.Serap Bulut© 2010, Hindawi Publishing Corporation. All rights reserved.