Keynes’ Lower-Upper Bound Interval Approach to Probability

2010 ◽  
Author(s):  
Rogério Arthmar ◽  
Michael Emmett Brady
Keyword(s):  
Upper Bound ◽  
Lower Upper ◽  
Interval Approach

scholarly journals Fast and accurate exercise policies for Bermudan swaptions in the LIBOR market model

2016 ◽  
Vol 03 (01) ◽  
pp. 1650005 ◽  
Author(s):  
Patrik Karlsson ◽  
Shashi Jain ◽  
Cornelis W. Oosterlee
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Monte Carlo Simulations ◽  
Upper Bound ◽  
Market Model ◽  
Monte Carlo Approach ◽  
Lower Upper ◽  
Libor Market Model ◽  
Bermudan Swaptions

This paper describes an American Monte Carlo approach for obtaining fast and accurate exercise policies for pricing of callable LIBOR Exotics (e.g., Bermudan swaptions) in the LIBOR market model using the Stochastic Grid Bundling Method (SGBM). SGBM is a bundling and regression based Monte Carlo method where the continuation value is projected onto a space where the distribution is known. We also demonstrate an algorithm to obtain accurate and tight lower–upper bound values without the need for nested Monte Carlo simulations.

A novel method based on lower–upper bound approximation to predict the wind energy

2020 ◽  
Vol 259 ◽  
pp. 120458
Author(s):  
Peng Wen ◽  
Su Zhang ◽  
Yazhou Xing ◽  
Limin Huo ◽  
Navid Bohlooli
Keyword(s):  
Wind Energy ◽  
Upper Bound ◽  
Lower Upper ◽  
Novel Method

Limit Analysis of Flow Through Inclined Converging Planes

1980 ◽  
Vol 102 (2) ◽  
pp. 109-117 ◽  
Author(s):  
M. Kiuchi ◽  
B. Avitzur
Keyword(s):  
Lower Bound ◽  
Plane Strain ◽  
Upper Bound ◽  
Limit Analysis ◽  
Velocity Fields ◽  
The Body ◽  
Design Flow ◽  
Upper And Lower Bounds ◽  
Lower Upper ◽  
Flow Through

A variety of mathematical models may be used to analyze plastic deformation during a metal-forming process. One of these methods—limit analysis—places the estimate of required power between an upper bound and a lower bound. The upper- and lower-bound analysis are designed so that the actual power or forming stress requirement is less than that predicted by the upper bound and greater than that predicted by the lower bound. Finding a lower upper-bound and a higher lower-bound reduces the uncertainty of the actual power requirement. Upper and lower bounds will permit the determination of such quantities as required forces, limitations on the process, optimal die design, flow patterns, and prediction and prevention of defects. Fundamental to the development of both upper-bound and lower-bound solutions is the division of the body into zones. For each of the zones there is written either a velocity field (upper bound) or a stress field (lower bound). A better choice of zones and fields brings the calculated values closer to actual values. In the present work, both upper- and lower-bound solutions are presented for plane-strain flow through inclined converging dies. For the upper bound, trapezoidal velocity fields, uni-triangular velocity fields, and multi-triangular velocity fields have been dealt with and the solutions compared to previously published work on cylindrical velocity fields. It was found that in different domains of the various combinations of the process parameters, different patterns of flow (cylindrical, triangular, etc.) provide lower upper-bound solutions. The lower-bound solution for plane-strain flow through inclined converging planes is newly developed.

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