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  • Odd Harmonic Numbers Exceed $10^{24}$ 
    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). ...
  • Ye olde Fibonacci curiosity shoppe revisited 
    Melham Ray (Fibonacci Association, 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 authors was to gather Fibonacci identities from ...
  • On a compositeness test for (2p+1)/3 
    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.
  • On a generalized fuzzy goal optimization for solving fuzzy multi-objective linear programming problems 
    Wu Fengjie; Lu Jie; Zhang Guangquan (IOS Press, 2006)
    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 ...
  • On an effective solution of the optimal stopping problem for random walks 
    Shiryaev Albert; Novikov Alex (Slack, Inc, 2005)
    We find a solution of the optimal stopping problem for the case when a reward function is an integer power function of a random walk on an infinite time interval. It is shown that an optimal stopping time is a first ...
  • On a new approach to calculating expectations for option pricing 
    Novikov Alex; Borovkov Kostya (Mathematics Education Research Group of Australasia, 2004)
    We discuss a simple new approach to calculating expectations of a specific form used for the pricing of derivative assets in financial mathematics. We show that in the 'vanilla case' , the expectations can be found by ...
  • On a Piece-Wise Deterministic Markov Process Model 
    Novikov Alex; Borovkov Kostya (Elsevier Science, 2002)
    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 ...
  • On a stochastic version of the trading rule 'Buy and Hold' 
    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 Blackâ¿¿Scholes model the drift term of the stock may change its value spontaneously at some random non-observable ...
  • On a theorem of GH Hardy concerning golf 
    Cohen Graeme (Mathematical Association, 2002)
  • On certain combinations of higher powers of Fibonacci numbers 
    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 ...
  • On Conditional Moments of GARCH Models, with Applications to Multiple Period Value at Risk Estimation 
    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 are ...
  • On Distributions Of First Passage Times And Optimal Stopping Of Ar(1) Sequences 
    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, ...
  • On EWMA procedure for detection of a change in observation via Martingale approach 
    Sukparungsee Saowanit; Novikov Alex (King Mongkut's Institute of Technology, Ladkrabang, Thailand, 2006)
    Using martingale technique, we present analytic approximations and exact lower bounds for the expectation of the first passage times of an Exponentially Weighted Moving Average (EWMA) procedure used for monitoring changes ...
  • On exit times of Levy-driven Ornstein-Uhlenbeck processes 
    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 ...
  • On filtering in Markovian term structure models: an approximation approach 
    Pasquali Sara; Chiarella Carl; Runggaldier Wolfgang (Australasian Medical Publishing Company, 2003)
    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 ...
  • On nonlinear models of markets with finite liquidity: Some cautionary notes 
    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 ...
  • On perfect totient numbers 
    Iannucci Douglas; Moujie Deng; Cohen Graeme (University of Waterloo, Ontario, Canada, 2003)
  • ON PRODUCT DIFFERENCE FIBONACCI IDENTITIES 
    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, ...
  • On Reciprocal Sums of Chebyshev Related Sequences 
    Melham Ray; Shannon Anthony (Fibonacci Assoc, 1995)
  • On semiparametric regression with O'Sullivan penalised splines 
    Wand Matt; 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 ...