A Forecasting Model for Stock Market Diversity

Sigrist, Fabio; Fernholz, Robert; Ferretti, Roberto

doi:10.1007/s10436-006-0046-y

Cited by 7 publications

(6 citation statements)

References 18 publications

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“…Proof. If N m−1 = N − 1 and N m = N , then by Lemma 4.2 we have z(X(T m +)) ∈ ∆ N,δ 0 + , thus µ (1)…”

Section: 33mentioning

confidence: 98%

“…In other words, immediately after any upward jump, the market weight process is in M δ 0 and µ (1) |N m−1 = N ) that the mth jump will be upward rather than downward, given that during the timeinterval (T m−1 , T m ) the market weight process µ(·) = z(X(·)) is at a given level N ∈ N.…”

Section: 31mentioning

confidence: 99%

“…Using (14), we can rewrite (41) in the notation of (11) [denoting by V (·) = {V (t), t ≥ 0} yet another one-dimensional standard {F(t)} t≥0 -Brownian motion] as d log µ (1)…”

Section: Appendix: a Comparison Lemmamentioning

confidence: 99%

“…the hitting time by Z(·) = log µ (1) (T (·)) of the level log(1 − δ). Therefore, by comparison (43), we have τ 0 ≤ ∆(τ ).…”

Section: Karatzas and A Sarantsevmentioning

confidence: 99%

“…This was shown in [8], Chapter 3; further examples of portfolios outperforming the market are given in [11,13], [12], Section 11. Some such models were constructed in [13,24,27,28] and [12], Chapter 9; see also the related articles [1,22].…”

mentioning

confidence: 99%

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Diverse market models of competing Brownian particles with splits and mergers

Karatzas¹,

Sarantsev²

2016

Ann. Appl. Probab.

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We study models of regulatory breakup, in the spirit of Strong and Fouque [Ann. Finance 7 (2011) 349-374] but with a fluctuating number of companies. An important class of market models is based on systems of competing Brownian particles: each company has a capitalization whose logarithm behaves as a Brownian motion with drift and diffusion coefficients depending on its current rank. We study such models with a fluctuating number of companies: If at some moment the share of the total market capitalization of a company reaches a fixed level, then the company is split into two parts of random size. Companies are also allowed to merge, when an exponential clock rings. We find conditions under which this system is nonexplosive (i.e., the number of companies remains finite at all times) and diverse, yet does not admit arbitrage opportunities.

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“…Proof. If N m−1 = N − 1 and N m = N , then by Lemma 4.2 we have z(X(T m +)) ∈ ∆ N,δ 0 + , thus µ (1)…”

Section: 33mentioning

confidence: 98%

Section: 31mentioning

confidence: 99%

“…Using (14), we can rewrite (41) in the notation of (11) [denoting by V (·) = {V (t), t ≥ 0} yet another one-dimensional standard {F(t)} t≥0 -Brownian motion] as d log µ (1)…”

Section: Appendix: a Comparison Lemmamentioning

confidence: 99%

“…the hitting time by Z(·) = log µ (1) (T (·)) of the level log(1 − δ). Therefore, by comparison (43), we have τ 0 ≤ ∆(τ ).…”

Section: Karatzas and A Sarantsevmentioning

confidence: 99%

mentioning

confidence: 99%

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Diverse market models of competing Brownian particles with splits and mergers

Karatzas¹,

Sarantsev²

2016

Ann. Appl. Probab.

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Information Geometry in Portfolio Theory

Wong

2018

Geometric Structures of Information

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On a class of diverse market models

Sarantsev

2013

Ann Finance

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A market model in Stochastic Portfolio Theory is a finite system of strictly positive stochastic processes. Each process represents the capitalization of a certain stock. If at any time no stock dominates almost the entire market, which means that its share of total market capitalization is not very close to one, then the market is called diverse. There are several ways to outperform diverse markets and get an arbitrage opportunity, and this makes these markets interesting. A feature of real-world markets is that stocks with smaller capitalizations have larger drift coefficients. Some models, like the Volatility-Stabilized Model, try to capture this property, but they are not diverse. In an attempt to combine this feature with diversity, we construct a new class of market models. We find simple, easy-to-test sufficient conditions for them to be diverse and other sufficient conditions for them not to be diverse.Keywords Stochastic Portfolio Theory · diverse markets · arbitrage opportunity · Feller's test JEL Classification Number G10 be the total capitalization of the market at time t and the market weights of stocks, respectively. Fix a threshold δ ∈ (0, 1). The market is called δ-diverse if for every t ≥ 0 and i = 1, . . . , n we have:This definition was introduced in [6]. Intuitively it means that, at any given moment, no stock dominates almost the entire market.

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A Forecasting Model for Stock Market Diversity

Abstract: Diversity, Generalized tree-structured threshold models, Maximum-likelihood estimation, Diversity-based portfolio strategies, C10, C13, C22, G11,

Cited by 7 publications

References 18 publications

Diverse market models of competing Brownian particles with splits and mergers

Diverse market models of competing Brownian particles with splits and mergers

Information Geometry in Portfolio Theory

On a class of diverse market models

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