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  • Cohen, Graeme; Sorli, Ronald (Amer Mathematical Soc, 2010)
    A number n > 1 is harmonic if sigma(n) vertical bar n tau(n), where tau(n) and sigma(n) are the number of positive divisors of n and their sum, respectively. It is known that there are no odd harmonic numbers up to 10(16). ...
  • Novikov, Alex; Shiryaev, Albert (Siam Publications, 2005)
    We find a solution of the optimal stopping problem for the case when a reward function is an integer function of a random walk on an infinite time interval. It is shown that an optimal stopping time is a first crossing ...
  • Borovkov, Kostya; Novikov, Alex (Mathematics Statistics, 2002)
  • Borovkov, Kostya; Novikov, Alex (Elsevier Science, 2001)
    We study a piece-wise deterministic Markov process having jumps of i.i.d. sizes with a constant intensity and decaying at a constant rate (a special case of a storage process with a general release rule). Necessary and ...
  • Shiryaev, Albert; Novikov, Alex (Oldenbourg Wissenschaftsverlag GmbH, 2009)
    The paper deals with the problem of finding an optimal one-time rebalancing strategy assuming that in the Blacka??Scholes model the drift term of the stock may change its value spontaneously at some random non-observable ...
  • Cohen, Graeme (The Mathematical Association, 2002)
  • Wong, Chi Ming; So, Mike (Institute of Statistical Science, Academia Sinica & International Chinese Statistical Association, 2003)
    In this article, the exact conditional second and fourth moments of returns and their temporal aggregates are derived under GARCH models. Three multiple period Value at Risk estimation methods are proposed. Two methods ...
  • Novikov, Alex (Siam Publications, 2009)
    Sufficient conditions for the exponential boundedness of first passage times of autoregressive (AR(1)) sequences are derived in this paper. An identity involving the mean of the first passage time is obtained. Further, ...
  • Suriyakat, Wannaporn; Areepong, Yupaporn; Sukparungsee, Saowanit; Mititelu, Gabriel (Academic Publications, 2012)
    In this paper, we use Fredholm second kind integral equations method to solve the corresponding Average Run Length (ARL), when the observations of a random process are serially-correlated. We derive explicit expressions ...
  • Sukparungsee, Saowanit; Novikov, Alex (King Mongkut's Institute of Technology, Ladkrabang, Thailand, 2006)
    Using martingale technique wepresent analytic approximation and exact lower bounds for the expectation of the first passage times of an Exponentially Weighted Moving Average (EWMA) procedure used for monitoring changes in ...
  • Borovkov, Kostya; Novikov, Alex (Elsevier B.V., 2008)
    We prove two martingale identities which involve exit times of Levy-driven Ornstein-Uhlenbeck processes. Using these identities we find an explicit formula for the Laplace transform of the exit time under the assumption ...
  • Chiarella, Carl; Pasquali, Sara; Runggaldier, Wolfgang (Applied Probability Trust, 2001)
    We consider a parametrization of the Heath-Jarrow-Morton (HJM) family of term structure of interest rate models that allows a finite-dimensional Markovian representation of the stochastic dynamics. This parametrization ...
  • Glover, Kristoffer; Duck, Peter; Newton, David (SIAM Publishing, 2010)
    The recent financial crisis and related liquidity issues have illuminated an urgent need for a better understanding of the effects of limited liquidity on all aspects of the financial system. This paper considers such ...
  • Wand, Matthew; Ormerod, J. (Blackwell Publishing Ltd, 2008)
    An exposition on the use of O'Sullivan penalized splines in contemporary semiparametric regression, including mixed model and Bayesian formulations, is presented. O'Sullivan penalized splines are similar to P-splines, but ...
  • Melham, Ray (European Mathematical Society Publishing House, 1999)
    ON SUMS OF POWERS OF TERMS IN A LINEAR RECURRENCE
  • Li, Weiye; Rychlik, Marek; Szidarovszky, Ferenc; Chiarella, Carl (Pergamon-Elsevier Science Ltd, 2003)
  • Milton, Graeme; Nicorovici, Nicolae (Royal Society, 2006)
    Regions of anomalous localized resonance, such as occurring near superlenses, are shown to lead to cloaking effects. This occurs when the resonant field generated by a polarizable line or point dipole acts back on the ...
  • Li, Sanjiang; Li, Yuefeng (Elsevier Science Inc, 2006)
    The importance of relational methods in temporal and spatial reasoning has been widely recognised in the last two decades. A quite large part of contemporary spatial reasoning is concerned with the research of relation ...
  • Shi, Chenggen; Zhang, Guangquan; Lu, Jie (Elsevier, 2005)
    Linear bilevel programming theory has been studied for many years by a number of researchers from different aspects, yet it still remains to some extent unsatisfactory and incomplete. The main challenge is how to solve a ...
  • Fergusson, Kevin; Platen, Eckhard (Routledge, 2006)
    In this paper distributions are identified which suitably fit log-returns of the world stock index when these are expressed in units of different currencies. By searching for a best fit in the class of symmetric generalized ...