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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). ...
  • Melham, Ray (Fibonacci Assoc, 2004)
    There are many Fibonacci identities to be found in short informal articles in the early editions of The Fibonacci Quarterly. See, for example, (1) and (2). The aim of the authoprs was to gather Fibonacci identities from ...
  • Berrizbeitia, Pedro; Luca, Florian; Melham, Ray (University of Waterloo, Ontario, Canada, 2010)
    n this note, we give a necessary condition for the primality of (2p+1)/3.
  • Lu, Jie; Wu, Fengiie; Zhang, Guangquan (IOS Press, 2007)
    Many organizational decision problems can be formulated by multi-objective linear programming (MOLP) models. Referring to the imprecision inherent in human judgments, uncertainty may be incorporated in the parameters of ...
  • 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)
  • Melham, Ray (Fibonacci Association, 2010)
    We present identities that we feel can be regarded as higher order analogues of the well-known identity F; + F;+l = Hn+l. We give three theorems corresponding to the powers 4, 6, and 8. We also state two conjectures that ...
  • So, Mike; Wong, Davy (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 ...
  • Iannucci, Douglas; Moujie, Deng; Cohen, Graeme (University of Waterloo, Ontario, Canada, 2003)
  • Melham, Ray (Walter de Gruyter GmbH & Co. KG, 2011)
    Simson's identity is a well-known Fibonacci identity in which the difference of certain order 2 products has a particularly pleasing form. Other old and beautiful identities of a similar nature are attributed to Catalan, ...
  • Melham, Ray; Shannon, Anthony (Fibonacci Assoc, 1995)