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 ...
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, ...
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 ...
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 ...
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 ...
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, ...
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 ...
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 ...
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 ...