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W. N. Bailey

Bio: W. N. Bailey is an academic researcher. The author has contributed to research in topics: Confluent hypergeometric function & Hypergeometric function. The author has an hindex of 1, co-authored 1 publications receiving 167 citations.

Papers
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Journal ArticleDOI
01 Jul 1960-Nature
TL;DR: In this paper, the Confluent Hypergeometric Functions (CGF) are used to express the hypergeometric functions of a given hypergeometrical function in the form of a convex polygon.
Abstract: Confluent Hypergeometric Functions By Dr L J Slater Pp ix + 247 (Cambridge: At the University Press, 1960) 65s net

194 citations


Cited by
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TL;DR: In this article, the authors proposed a new approach to sparsity called the horseshoe estimator, which is a member of the same family of multivariate scale mixtures of normals.
Abstract: This paper proposes a new approach to sparsity called the horseshoe estimator. The horseshoe is a close cousin of other widely used Bayes rules arising from, for example, double-exponential and Cauchy priors, in that it is a member of the same family of multivariate scale mixtures of normals. But the horseshoe enjoys a number of advantages over existing approaches, including its robustness, its adaptivity to dierent sparsity patterns, and its analytical tractability. We prove two theorems that formally characterize both the horseshoe’s adeptness at large outlying signals, and its super-ecient rate of convergence to the correct estimate of the sampling density in sparse situations. Finally, using a combination of real and simulated data, we show that the horseshoe estimator corresponds quite closely to the answers one would get by pursuing a full Bayesian model-averaging approach using a discrete mixture prior to model signals and noise.

1,260 citations

Journal ArticleDOI
TL;DR: The bit error rate (BER) performance of an M-branch maximal-ratio combiner (MRC) for the detection of signals in a correlated Nakagami-fading channel is analyzed and outage probabilities are calculated for the digital radio communication systems via the correlated fading channel.
Abstract: The bit error rate (BER) performance of an M-branch maximal-ratio combiner (MRC) for the detection of signals in a correlated Nakagami-fading channel is analyzed. Coherent and incoherent detection of frequency shift-keying (FSK) and phase-shift keying (PSK) signals are considered. It is assumed that the fading parameters in each diversity branch are identical. The effect of correlation is studied by assuming two types of correlation among the quadrature components of the signals in each diversity branch. Outage probabilities are also calculated for the digital radio communication systems via the correlated fading channel. >

470 citations

Journal ArticleDOI
TL;DR: It is demonstrated that the prices of options, which depend on extrema, can be much more sensitive to the specification of the underlying price process than standard call and put options and show that a financial institution that uses the standard geometric Brownian motion assumption is exposed to significant pricing and hedging errors when dealing in path-dependent options.
Abstract: Much of the work on path-dependent options assumes that the underlying asset price follows geometric Brownian motion with constant volatility. This paper uses a more general assumption for the asset price process that provides a better fit to the empirical observations. We use the so-called constant elasticity of variance CEV diffusion model where the volatility is a function of the underlying asset price. We derive analytical formulae for the prices of important types of path-dependent options under this assumption. We demonstrate that the prices of options, which depend on extrema, such as barrier and lookback options, can be much more sensitive to the specification of the underlying price process than standard call and put options and show that a financial institution that uses the standard geometric Brownian motion assumption is exposed to significant pricing and hedging errors when dealing in path-dependent options.

347 citations

Journal ArticleDOI
TL;DR: An identity in law is used between the integral of geometric Brownian motion over a finite time interval [0,t] and the state at timet of a one-dimensional diffusion process with affine drift and linear diffusion to express Asian option values in terms of spectral expansions associated with the diffusion infinitesimal generator.
Abstract: Arithmetic Asian or average price options deliver payoffs based on the average underlying price over a prespecified time period. Asian options are an important family of derivative contracts with a wide variety of applications in currency, equity, interest rate, commodity, energy, and insurance markets. We derive two analytical formulas for the value of the continuously sampled arithmetic Asian option when the underlying asset price follows geometric Brownian motion. We use an identity in law between the integral of geometric Brownian motion over a finite time interval [0,t] and the state at timet of a one-dimensional diffusion process with affine drift and linear diffusion and express Asian option values in terms of spectral expansions associated with the diffusion infinitesimal generator. The first formula is an infinite series of terms involving Whittaker functionsM andW. The second formula is a single real integral of an expression involving Whittaker functionW plus (for some parameter values) a finite number of additional terms involving incomplete gamma functions and Laguerre polynomials. The two formulas allow accurate computation of continuously sampled arithmetic Asian option prices.

258 citations

Posted Content
TL;DR: In this paper, the exchange rate dynamics in alternative cases where the authorities promise to confine a floating rate within a predetermined range and peg the currency once it reaches a predetermined future level are examined.
Abstract: Techniques of regulated Brownian motion are used to analyze the behavior of the exchange rate when official policy reaction functions are subject to future stochastic changes. We examine exchange-rate dynamics in alternative cases where the authorities promise (i) to confine a floating rate within a predetermined range and (ii) to peg the currency once it reaches a predetermined future level. Similarities between these and several related examples of regime switching are stressed

221 citations