The Numerical Evaluation of Certain Multivariate Normal Integrals

Curnow, R. N.; Dunnett, Charles W.

doi:10.1214/aoms/1177704581

Cited by 94 publications

(37 citation statements)

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“…then a computational load to evaluate n dimensional normal probability integrals reduces to be n /2 or( n -1)/2 dimensional probability integrals (12) (13) . However, it consumes still much time to calculate n SO when n is more than 5 because of multiple integrals.…”

Section: Somentioning

confidence: 99%

A Two Stage Solution Procedure for Production Planning System with Advance Demand Information

Ueno¹,

Kadomoto²,

Hasuike

et al. 2012

JAMDSM

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We model for 'Naiji System' which is a unique corporation technique between a manufacturer and suppliers in Japan. We propose a two stage solution procedure for a production planning problem with advance demand information, which is called 'Naiji'. Under demand uncertainty, this model is formulated as a nonlinear stochastic programming problem which minimizes the sum of production cost and inventory holding cost subject to a probabilistic constraint and some linear production constraints. By the convexity and the special structure of correlation matrix in the problem where inventory for different periods is not independent, we propose a solution procedure with two stages which are named Mass Customization Production Planning & Management System (MCPS) and Variable Mesh Neighborhood Search (VMNS) based on meta-heuristics. It is shown that the proposed solution procedure is available to get a near optimal solution efficiently and practical for making a good master production schedule in the suppliers.

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Section: Somentioning

confidence: 99%

A Two Stage Solution Procedure for Production Planning System with Advance Demand Information

Ueno¹,

Kadomoto²,

Hasuike

et al. 2012

JAMDSM

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show abstract

“…Let the correlation matrix be non-singular and ρ 11 = 1. Under these conditions Curnow and Dunnett [3] derive the following reduction formula…”

Section: The Curnow and Dunnett Integral Reduction Techniquementioning

confidence: 99%

Instalment Options: A Closed-Form Solution and the Limiting Case

Griebsch

Kühn

Wystup

2008

Mathematical Control Theory and Finance

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In Foreign Exchange Markets Compound options (options on options) are traded frequently. Instalment options generalize the concept of Compound options as they allow the holder to prolong a Vanilla Call or Put option by paying instalments of a discrete payment plan. We derive a closed-form solution to the value of such an option in the Black-Scholes model and prove that the limiting case of an Instalment option with a continuous payment plan is equivalent to a portfolio consisting of a European Vanilla option and an American Put on this Vanilla option with a time-dependent strike.

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“…Martin and Wilson computed an approximation to the probability of selection due to Curnow and Dunnett (1962). Owing to advances in computation, it is possible to obtain accurate estimates of multidimensional integrals (NAG, 1984) without excessive computer time.…”

Section: Calculationmentioning

confidence: 99%

“…Second, Martin and Wilson employed a form of "soft selection" in which the probability of selection varied in a sigmoid fashion over the range of the character. This selection function was based on a model described by Curnow and Dunnett (1962). In this model, the observed variate, y, comprises a value x on an underlying distribution of liability, and a random error component z. Truncate (hard) selection is applied to the y variate to effect a sigmoid function of selection on the underlying variate, x.…”

Section: Introductionmentioning

confidence: 99%