2012
DOI: 10.1007/978-3-642-25746-9_6
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Optimal Delaunay and Voronoi Quantization Schemes for Pricing American Style Options

Abstract: We review in this article pure quantization methods for the pricing of multiple exercise options. These quantization methods have the common advantage, that they allow a straightforward implementation of the Backward Dynamic Programming Principle for optimal stopping and stochastic control problems. Moreover we present here for the first time a unified discussion of this topic for Voronoi and Delaunay quantization and illustrate the performances of both methods by several numerical examples.

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Cited by 28 publications
(31 citation statements)
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“…Optimal transport [22,16] is a blossoming subject that has known major breakthroughs these last decades. Its applications range from finance [23], mesh generation [11], PDE analysis [15] and imaging [24,28] to machine learning and clustering [26,12]. This paper is limited to the semi-discrete case, which consists in transporting discrete measures (Dirac masses) towards a background measure.…”
Section: Introductionmentioning
confidence: 99%
“…Optimal transport [22,16] is a blossoming subject that has known major breakthroughs these last decades. Its applications range from finance [23], mesh generation [11], PDE analysis [15] and imaging [24,28] to machine learning and clustering [26,12]. This paper is limited to the semi-discrete case, which consists in transporting discrete measures (Dirac masses) towards a background measure.…”
Section: Introductionmentioning
confidence: 99%
“…The study of this typical cell in the literature includes mean values calculations [20], second order properties [14] and distributional estimates [5,21]. Voronoi tessellations are extensively used in many domains such as cellular biology [25], astrophysics [32], telecommunications [3] and finance [23]. For a complete account on Poisson-Voronoi tessellations and their applications, we refer to the book by Okabe et al (see Chapter 5 in [22]).…”
Section: Introductionmentioning
confidence: 99%
“…Unfortunately, it is satisfied only by few quantizers. A new notion of quantization, called dual quantization has been recently developed (see [64] for a theoretical introduction and [63,65] for applications to Numerical Probability) in which a reverse stationarity property is satisfied by all dual quantizers. Typically for dual quantization, one has…”
Section: Remarksmentioning
confidence: 99%
“…For more details we refer to [2][3][4]65] (the last reference is devoted to both Voronoi and dual vector quantizations applied to the the pricing of American style derivatives) and [19,62,68] (for non-linear filtering, stochastic control applied to Finance) and the references therein.…”
Section: Among Others For Details) This (Approximately) Leads Tomentioning
confidence: 99%