http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2012, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijsa/2012/258415/We consider a one-dimensional stochastic equation dXt=b(t,Xt−)dZt+a(t,Xt)dt, t≥0, with respect to a symmetric stable process Z of index 0<α≤2. It is shown that solving this equation is equivalent to solving of a 2-dimensional stochastic equation dLt=B(Lt−)dWt with respect to the semimartingale W=(Z,t) and corresponding matrix B. In the case of 1≤α<2 we provide new sufficient conditions for the existence of solutions of both equations with measurable coefficients. The existence proofs are established using the method of Krylov's estimates for processes satisfying the 2-dimensional equation. On another hand, the Krylov's estimates are based on some analytical facts of independent interest that are also proved in the paper.V. P. KurenokCopyright © 2012 V. P. Kurenok. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/942478/We consider harvesting in the Black-Scholes Quanto Market when the exchange rate is being modeled by the process Et=E0exp⁡{Xt}, where Xt is a semimartingale, and we ask the following question: What harvesting strategy γ* and the value function Φ maximize the expected total income of an investment? We formulate a singular stochastic control problem and give sufficient conditions for the existence of an optimal strategy. We found that, if the value function is not too sensitive to changes in the prices of the investments, the problem reduces to that of Lungu and Øksendal. However, the general solution of this problem still remains elusive.E. R. Offen and E. M. LunguCopyright © 2011 E. R. Offen and E. M. Lungu. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/840908/We obtain a large deviation principle for the stochastic differential equations on the sphere Sd associated with the critical Sobolev Brownian vector fields.Qinghua WangCopyright © 2011 Qinghua Wang. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/843246/Should the regime-switching risk be priced? This is perhaps one of the important “normative” issues to be addressed in pricing contingent claims under a Markovian, regime-switching, Black-Scholes-Merton model. We address this issue using a minimal relative entropy approach. Firstly, we apply a martingale representation for a double martingale to characterize the canonical space of equivalent martingale measures which may be viewed as the largest space of equivalent martingale measures to incorporate both the diffusion risk and the regime-switching risk. Then we show that an optimal equivalent martingale measure over the canonical space selected by minimizing the relative entropy between an equivalent martingale measure and the real-world probability measure does not price the regime-switching risk. The optimal measure also justifies the use of the Esscher transform for option valuation in the regime-switching market.Tak Kuen SiuCopyright © 2011 Tak Kuen Siu. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/543590/We consider an agent who wants to liquidate an asset with unknown drift. The agent believes that the drift takes one of two given values and has initially an estimate for the probability of either of them. As time goes by, the agent observes the asset price and can therefore update his beliefs about the probabilities for the drift distribution. We formulate an optimal stopping problem that describes the liquidation problem, and we demonstrate that the optimal strategy is to liquidate the first time the asset price falls below a certain time-dependent boundary. Moreover, this boundary is shown to be monotonically increasing, continuous and to satisfy a nonlinear integral equation.Erik Ekström and Bing LuCopyright © 2011 Erik Ekström and Bing Lu. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/762486/Let (B(t))t∈[0,1] be the linear Brownian motion and (Xn(t))t∈[0,1] the (n−1)-fold integral of Brownian motion, with n being a positive integer: Xn(t)=∫0t((t−s)n−1/(n−1)!)dB(s) for any t∈[0,1]. In this paper we construct several bridges between times 0 and 1 of the process (Xn(t))t∈[0,1] involving conditions on the successive derivatives of Xn at times 0 and 1. For this family of bridges, we make a correspondence with certain boundary value problems related to the one-dimensional polyharmonic operator. We also study the classical problem of prediction. Our results involve various Hermite interpolation polynomials.Aimé LachalCopyright © 2011 Aimé Lachal. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/784638/We discuss existence results of mild solutions for stochastic differential inclusions subject to nonlocal conditions. We provide sufficient conditions in order to obtain a priori bounds on possible solutions of a one-parameter family of problems related to the original one. We, then, rely on fixed point theorems for multivalued operators to prove our main results.A. Vinodkumar and A. BoucherifCopyright © 2011 A. Vinodkumar and A. Boucherif. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/916952/We consider Pλ,τM policy of a dam in which the water input is an increasing Lévy process. The release rate of the water is changed from 0 to M and from M to 0 (M>0) at the moments when the water level upcrosses level λ and downcrosses level τ   (τ<λ), respectively. We determine the potential of the dam content and compute the total discounted as well as the long-run average cost. We also find the stationary distribution of the dam content. Our results extend the results in the literature when the water input is assumed to be a Poisson process.Mohamed Abdel-HameedCopyright © 2011 Mohamed Abdel-Hameed. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/186206/This paper studies the existence and uniqueness of a mild solution for a neutral stochastic partial functional differential equation using a local Lipschitz condition. When the neutral term is zero and even in the deterministic special case, the result obtained here appears to be new. An example is included to illustrate the theory.T. E. GovindanCopyright © 2011 T. E. Govindan. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/151823/The standard Yule-Walker equations, as they are known for an autoregression, are generalized to involve the moments of a moving-average process indexed on any number of dimensions. Once observations become available, new moments estimators are set to imitate the theoretical equations. These estimators are not only consistent but also asymptotically normal for any number of indexes. Their variance matrix resembles a standard result from maximum Gaussian likelihood estimation. A simulation study is added to conclude on their efficiency.Chrysoula Dimitriou-FakalouCopyright © 2011 Chrysoula Dimitriou-Fakalou. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/801303/On a weakly Blackwell space we show how to define a Markov chain approximating problem, for the target problem. The approximating problem is proved to converge to the optimal reduced problem under different pseudometrics.Giacomo Aletti and Diane SaadaCopyright © 2011 Giacomo Aletti and Diane Saada. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/190603/We consider an insurance company whose surplus follows a diffusion process with proportional reinsurance and impulse dividend control. Our objective is to maximize expected discounted dividend payouts to shareholders of the company until the time of bankruptcy. To meet some essential requirements of solvency control (e.g., bankruptcy not soon), we impose some constraints on the insurance company's dividend policy. Under two types of constraints, we derive the value functions and optimal control policies of the company.Hui Meng and Tak Kuen SiuCopyright © 2011 Hui Meng and Tak Kuen Siu. All rights reserved.http://www.hindawi.com/journals/ijsa/2012/697458/We consider the best-choice problem with disorder and imperfect observation. The decision-maker observes sequentially a known number of i.i.d random variables from a known distribution with the object of choosing the largest. At the random time the distribution law of observations is changed. The random variables cannot be perfectly observed. Each time a random variable is sampled the decision-maker is informed only whether it is greater than or less than some level specified by him. The decision-maker can choose at most one of the observation. The optimal rule is derived in the class of Bayes' strategies.Vladimir Mazalov and Evgeny IvashkoCopyright © 2012 Vladimir Mazalov and Evgeny Ivashko. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/605068/We consider nonconservative diffusion processes xt on the unit interval, so with absorbing barriers. Using Doob-transformation techniques involving superharmonic functions, we modify the original process to form a new diffusion process xt∼ presenting an additional killing rate part d>0. We limit ourselves to situations for which xt∼ is itself nonconservative with upper bounded killing rate. For this transformed process, we study various conditionings on events pertaining to both the killing and the absorption times. We introduce the idea of a reciprocal Doob transform: we start from the process xt∼, apply the reciprocal Doob transform ending up in a new process which is xt but now with an additional branching rate b>0, which is also upper bounded. For this supercritical binary branching diffusion, there is a tradeoff between branching events giving birth to new particles and absorption at the boundaries, killing the particles. Under our assumptions, the branching diffusion process gets eventually globally extinct in finite time. We apply these ideas to diffusion processes arising in population genetics. In this setup, the process xt is a Wright-Fisher diffusion with selection. Using an exponential Doob transform, we end up with a killed neutral Wright-Fisher diffusion xt∼. We give a detailed study of the binary branching diffusion process obtained by using the corresponding reciprocal Doob transform.Thierry E. HuilletCopyright © 2011 Thierry E. Huillet. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/576791/We propose a continuous-time autoregressive model for the temperature dynamics with volatility being the product of a seasonal function and a stochastic process. We use the Barndorff-Nielsen and Shephard model for the stochastic volatility. The proposed temperature dynamics is flexible enough to model temperature data accurately, and at the same time being analytically tractable. Futures prices for commonly traded contracts at the Chicago Mercantile Exchange on indices like cooling- and heating-degree days and cumulative average temperatures are computed, as well as option prices on them.Fred Espen Benth and Jūratė Šaltytė BenthCopyright © 2011 Fred Espen Benth and Jūratė Šaltytė Benth. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/721352/We have studied dynamics of both internal and external noises-driven dynamical system in terms of information entropy at both nonstationary and stationary states. Here a unified description of entropy flux and entropy production is considered. Based on the Fokker-Planck description of stochastic processes and the entropy balance equation we have calculated time dependence of the information entropy production and entropy flux in presence and absence of nonequilibrium constraint (NEC). In the presence of NEC we have observed extremum behavior in the variation of entropy production as function of damping strength, noise correlation, and non-Gaussian parameter (which determine the deviation of external noise behavior from Gaussian characteristic), respectively. Thus the properties of noise process are important for entropy production.Monoj Kumar Sen, Alendu Baura, and Bidhan Chandra BagCopyright © 2011 Monoj Kumar Sen et al. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/803683/In (Chen and Kulik, 2009), a method of renormalization was proposed for constructing some more physically realistic random potentials in a Poisson cloud. This paper is devoted to the detailed analysis of the asymptotic behavior of the annealed negative exponential moments for the Brownian motion in a renormalized Poisson potential. The main results of the paper are applied to studying the Lifshitz tails asymptotics of the integrated density of states for random Schrödinger operators with their potential terms represented by renormalized Poisson potentials.Xia Chen and Alexey KulikCopyright © 2011 Xia Chen and Alexey Kulik. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/469806/We consider the Cauchy-Dirichlet problem in [0,∞)×D for a class of linear parabolic partial differential equations. We assume that D⊂ℝd is an unbounded, open, connected set with regular boundary. Our hypotheses are unbounded and locally Lipschitz coefficients, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution to the nonhomogeneous Cauchy-Dirichlet problem using stochastic differential equations and parabolic differential equations in bounded domains.Gerardo RubioCopyright © 2011 Gerardo Rubio. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/435145/We study the valuation of the variance swaps under stochastic volatility with delay and jumps. In our model, the volatility of the underlying stock price process not only incorporates jumps, which are found to be active empirically, but also exhibits past dependence: the behavior of a stock price right after a given time t depends not only on the situation at t but also on the whole past (history) of the process S(t) up to time t as well. The jump part in our model is finally represented by a general version of compound Poisson processes. We provide some analytical closed forms for the expectation of the realized variance for the stochastic volatility with delay and jumps. We also present a lower bound for delay as a measure of risk. As applications of our analytical solutions, a numerical example using S&P60 Canada Index (1998–2002) is then provided to price variance swaps.Anatoliy Swishchuk and Li XuCopyright © 2011 Anatoliy Swishchuk and Li Xu. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/390548/We provide a stochastic analysis of hard disk performance, including a closed form solution for the average access time of a memory request. The model we use covers a wide range of types and applications of disks, and in particular it captures modern innovations like zone bit recording. The derivation is based on an analytical technique we call “shuffling”, which greatly simplifies the analysis relative to previous work and provides a simple, easy-to-use formula for the average access time. Our analysis can predict performance of single disks for a wide range of disk types and workloads. Furthermore, it can predict the performance benefits of several optimizations, including short stroking and mirroring, which are common in disk arrays.Field Cady, Yi Zhuang, and Mor Harchol-BalterCopyright © 2011 Field Cady et al. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/296259/Let X(t) be a controlled one-dimensional standard Brownian motion starting from x∈(−d,d). The problem of optimally controlling X(t) until |X(t)|=d for the first time is solved explicitly in a particular case. The maximal value that the instantaneous reward given for survival in (−d,d) can take is determined.Mario LefebvreCopyright © 2011 Mario Lefebvre. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/489386/The object of this paper is to study the stability behaviours of the deterministic and stochastic versions of a two-species symmetric competition model. The logistic parameters of the competitive species are perturbed by colored noises or Ornstein-Uhlenbeck processes due to random environment. The Fokker-Planck equation has been used to obtain probability density functions. Here, we have also discussed the relationship between stability behaviours of this model in a deterministic environment and the corresponding model in a stochastic environment.G. P. SamantaCopyright © 2011 G. P. Samanta. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/797656/We use the q-Weibull distribution and define a new counting process using the fractional order. As a consequence, we introduce a q-process with q-Weibull interarrival times. Some interesting special cases are also discussed which leads to a Mittag-Leffler form.Kunnummal Muralidharan and Seema S. NairCopyright © 2011 Kunnummal Muralidharan and Seema S. Nair. All rights reserved.http://www.hindawi.com/journals/ijsa/2011/501360/Using an integral equation associated with generalized backward Kolmogorov's equation for the transition probability density function, recurrence relations are derived for the moments of the time of first exit of jump-diffusions with Markovian switching. The results are used to find the expectation of first passage time of some financial models.Jun Peng and Zaiming LiuCopyright © 2011 Jun Peng and Zaiming Liu. All rights reserved.http://www.hindawi.com/journals/ijsa/2010/347105/We consider the geometric Markov renewal processes as a model for a security market and study this processes in a diffusion approximation scheme. Weak convergence analysis and rates of convergence of ergodic geometric Markov renewal processes in diffusion scheme are presented. We present European call option pricing formulas in the case of ergodic, double-averaged, and merged diffusion geometric Markov renewal processes.Anatoliy Swishchuk and M. Shafiqul IslamCopyright © 2010 Anatoliy Swishchuk and M. Shafiqul Islam. All rights reserved.http://www.hindawi.com/journals/ijsa/2010/870516/We investigate a Markov, regime-switching, marked point process for the short-term interest rate in a market. The intensity of the marked point process is a bounded, predictable process and is modulated by two observable factors. One is an economic factor described by a diffusion process, and another one is described by a Markov chain. The states of the chain are interpreted as different rating categories of corporate credit ratings issued by rating agencies. We consider a general pricing kernel which can explicitly price economic, market, and credit risks. It is shown that the price of a pure discount bond satisfies a system of coupled partial differential-integral equations under a risk-adjusted measure.Tak Kuen SiuCopyright © 2010 Tak Kuen Siu. All rights reserved.http://www.hindawi.com/journals/ijsa/2010/217372/We establish the existence of a stochastic integral in a nuclear space setting as follows. Let E, F, and G be nuclear spaces which satisfy the following conditions: the spaces are reflexive, complete, bornological spaces such that their strong duals also satisfy these conditions. Assume that there is a continuous bilinear mapping of E×F into G. If H is an integrable, E-valued predictable process and X is an F-valued square integrable martingale, then there exists a G-valued process (∫HdX)t called the stochastic integral. The Lebesgue space of these integrable processes is studied and convergence theorems are given. Extensions to general locally convex spaces are presented.J. K. Brooks and J. T. KozinskiCopyright © 2010 J. K. Brooks and J. T. Kozinski. All rights reserved.http://www.hindawi.com/journals/ijsa/2010/697257/We investigate a continuous-time version of the mean-variance portfolio selection model with jumps under regime switching. The portfolio selection is proposed and analyzed for a market consisting of one bank account and multiple stocks. The random regime switching is assumed to be independent of the underlying Brownian motion and jump processes. A Markov chain modulated diffusion formulation is employed to model the problem.Lin ZhaoCopyright © 2010 Lin Zhao. All rights reserved.http://www.hindawi.com/journals/ijsa/2010/730492/The existence and uniqueness of adapted solutions to the backward stochastic Navier-Stokes equation with artificial compressibility in two-dimensional bounded domains are shown by Minty-Browder monotonicity argument, finite-dimensional projections, and truncations. Continuity of the solutions with respect to terminal conditions is given, and the convergence of the system to an incompressible flow is also established.Hong YinCopyright © 2010 Hong Yin. All rights reserved.http://www.hindawi.com/journals/ijsa/2010/329185/In the first part of the paper we obtain existence and characterizations of an optimal control for a linear quadratic control problem of linear stochastic Volterra equations. In the second part, using the Malliavin calculus approach, we deduce a general maximum principle for optimal control of general stochastic Volterra equations. The result is applied to solve some stochastic control problem for some stochastic delay equations.Bernt øksendal and Tusheng ZhangCopyright © 2010 Bernt øksendal and Tusheng Zhang. All rights reserved.