Results 11  20
of
406
Hypergeometrics and the Cost Structure of Quadtrees
, 1995
"... Several characteristic parameters of randomly grown quadtrees of any dimension are analyzed. Additive parameters have expectations whose generating functions are expressible in terms of generalized hypergeometric functions. A complex asymptotic process based on singularity analysis and integral repr ..."
Abstract

Cited by 27 (3 self)
 Add to MetaCart
Several characteristic parameters of randomly grown quadtrees of any dimension are analyzed. Additive parameters have expectations whose generating functions are expressible in terms of generalized hypergeometric functions. A complex asymptotic process based on singularity analysis and integral representations akin to Mellin transforms leads to explicit values for various structure constants related to path length, retrieval costs, and storage occupation.
Enumeration of Lozenge Tilings of Hexagons with a Central Triangular Hole
"... . We deal with the unweighted and weighted enumerations of lozenge tilings of a hexagon with side lengths a; b + m; c; a + m; b; c + m, where an equilateral triangle of side length m has been removed from the center. We give closed formulas for the plain enumeration and for a certain (\Gamma1)enume ..."
Abstract

Cited by 25 (9 self)
 Add to MetaCart
. We deal with the unweighted and weighted enumerations of lozenge tilings of a hexagon with side lengths a; b + m; c; a + m; b; c + m, where an equilateral triangle of side length m has been removed from the center. We give closed formulas for the plain enumeration and for a certain (\Gamma1)enumeration of these lozenge tilings. In the case that a = b = c, we also provide closed formulas for certain weighted enumerations of those lozenge tilings that are cyclically symmetric. For m = 0, the latter formulas specialize to statements about weighted enumerations of cyclically symmetric plane partitions. One such specialization gives a proof of a conjecture of Stembridge on a certain weighted count of cyclically symmetric plane partitions. The tools employed in our proofs are nonstandard applications of the theory of nonintersecting lattice paths and determinant evaluations. In particular, we evaluate the determinants det 0i;jn\Gamma1 \Gamma !ffi ij + \Gamma m+i+j j \Delta\Delta , w...
Pricing options on scalar diffusions: an eigenfunction expansion approach
 Management Science
"... This paper develops an eigenfunction expansion approach to pricing options on scalar diffusion processes. All derivative securities are unbundled into portfolios of primitive securities termed eigensecurities. Eigensecurities are eigenvectors of the pricing operator (present value operator). Pricing ..."
Abstract

Cited by 24 (9 self)
 Add to MetaCart
This paper develops an eigenfunction expansion approach to pricing options on scalar diffusion processes. All derivative securities are unbundled into portfolios of primitive securities termed eigensecurities. Eigensecurities are eigenvectors of the pricing operator (present value operator). Pricing is then immediate by the linearity property of the pricing operator and the eigenvector property of eigensecurities. To illustrate the computational power of the method, we develop two applications: pricing vanilla, single and doublebarrier options under the constant elasticity of variance (CEV) process and interest rate knockout options in the CoxIngersollRoss (CIR) termstructure model.
Expansion around halfinteger values, binomial sums and inverse binomial sums
 J. Math. Phys
, 2004
"... binomial sums ..."
(Show Context)
The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis
"... Abstract. We compute the number of rhombus tilings of a hexagon with sides N, M, N, N, M, N, which contain a fixed rhombus on the symmetry axis that cuts through the sides of length M. 1. ..."
Abstract

Cited by 23 (7 self)
 Add to MetaCart
Abstract. We compute the number of rhombus tilings of a hexagon with sides N, M, N, N, M, N, which contain a fixed rhombus on the symmetry axis that cuts through the sides of length M. 1.
2001), ‘Pricing and hedging pathdependent options under the CEV process
 Management Science
"... Much of the work on pathdependent options assumes that the underlying asset pricefollows 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 socalled constant ..."
Abstract

Cited by 22 (0 self)
 Add to MetaCart
(Show Context)
Much of the work on pathdependent options assumes that the underlying asset pricefollows 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 socalled 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 pathdependent 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 pathdependent options.
Determinant Identities And A Generalization Of The Number Of Totally Symmetric SelfComplementary Plane Partitions
"... We prove a constant term conjecture of Robbins and Zeilberger (J. Cambin. ..."
Abstract

Cited by 22 (13 self)
 Add to MetaCart
We prove a constant term conjecture of Robbins and Zeilberger (J. Cambin.
The Incomplete Gamma Functions Since Tricomi
 In Tricomi's Ideas and Contemporary Applied Mathematics, Atti dei Convegni Lincei, n. 147, Accademia Nazionale dei Lincei
, 1998
"... The theory of the incomplete gamma functions, as part of the theory of conuent hypergeometric functions, has received its rst systematic exposition by Tricomi in the early 1950s. His own contributions, as well as further advances made thereafter, are surveyed here with particular emphasis on asy ..."
Abstract

Cited by 21 (1 self)
 Add to MetaCart
The theory of the incomplete gamma functions, as part of the theory of conuent hypergeometric functions, has received its rst systematic exposition by Tricomi in the early 1950s. His own contributions, as well as further advances made thereafter, are surveyed here with particular emphasis on asymptotic expansions, zeros, inequalities, computational methods, and applications.
On the qanalog of Kummer’s theorem and applications
 Duke Math. J
, 1973
"... Saalschutz’s summation of 3F2[a, b,n; c, a b c n 1; 1] are well known,namely, E. Heine [8; p. 107, Equation (6)] showed that(1.1) 21Ia ’ b;q’c/ablc (c/a)(c/b).__(c)(c/ab) where and (a). (a; q), (1a)(1aq) (1aqa), (a) (a; q),(R) lim,. (a),. (See also [12; p. 97, Equation (3.3.2.2)].) F. H. Jack ..."
Abstract

Cited by 18 (2 self)
 Add to MetaCart
Saalschutz’s summation of 3F2[a, b,n; c, a b c n 1; 1] are well known,namely, E. Heine [8; p. 107, Equation (6)] showed that(1.1) 21Ia ’ b;q’c/ablc (c/a)(c/b).__(c)(c/ab) where and (a). (a; q), (1a)(1aq) (1aqa), (a) (a; q),(R) lim,. (a),. (See also [12; p. 97, Equation (3.3.2.2)].) F. H. Jackson [9; p. 145] showed that
Elementary Derivations of Summation and Transformation Formulas for QSeries
, 1995
"... this paper were presented, along with related exercises, in the author's minicourse on "qSeries" at the Fields Institute miniprogram on "Special Functions, qSeries and Related Topics," June 12 14, 1995. As is customary, we employ the notations used in BHS for the shifted ..."
Abstract

Cited by 17 (0 self)
 Add to MetaCart
this paper were presented, along with related exercises, in the author's minicourse on "qSeries" at the Fields Institute miniprogram on "Special Functions, qSeries and Related Topics," June 12 14, 1995. As is customary, we employ the notations used in BHS for the shifted factorial