Random Portfolios for Performance Measurement

Burns, Patrick

doi:10.1007/3-540-36626-1_11

Cited by 7 publications

(1 citation statement)

References 10 publications

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“…There is also little study about uniformly generating random points over the intersections of simplexes and simple convex bodies such as polytopes, although it has several applications, for example, in portfolio optimization (Dawson and Young 2003;Pouchkarev 2005;Burns 2007); in multicriteria decision analysis with imprecise weights (Park and Kim 1997;Butler et al 1997;Lahdelma et al 1998;Jia et al 1998;Lahdelma and Salminen 2009;Vetschera et al 2010;Tervonen et al 2013); in decision problems involving discrete joint probability distributions with imprecise probabilities (Walley 1991;Jeleva and Villeneuve 2004;Utkin and Coolen 2007;Montiel and Bickel 2013) or in design of mixture experiments (Tian et al 2009). …”

Section: Introductionmentioning

confidence: 98%

An economical acceptance–rejection algorithm for uniform random variate generation over constrained simplexes

Ahmadi‐Javid

Moeini

2015

Stat Comput

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This paper develops an algorithm for uniform random generation over a constrained simplex, which is the intersection of a standard simplex and a given set. Uniform sampling from constrained simplexes has numerous applications in different fields, such as portfolio optimization, stochastic multi-criteria decision analysis, experimental design with mixtures and decision problems involving discrete joint distributions with imprecise probabilities. The proposed algorithm is developed by combining the acceptancerejection and conditional methods along with the use of optimization tools. The acceptance rate of the algorithm is analytically compared to that of a crude acceptance-rejection algorithm, which generates points over the simplex and then rejects any points falling outside the intersecting set. Finally, using convex optimization, the setup phase of the algorithm is detailed for the special cases where the intersecting set is a general convex set, a convex set defined by a finite number of convex constraints or a polyhedron.Keywords Uniform random variate generation over simplexes · Convex optimization · Simulation-based portfolio optimization · Stochastic multi-criteria decision analysis · Distributions with imprecise probabilities ·

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