Stochastic Portfolio Theory

By E. Fernholz. 2002

380 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/a546d2e26962046148fc76617ccb01c24eb7d3ff

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In Management Science and Operations Research

Citations in the corpus

HEDGING UNDER ARBITRAGE (2010, neutral): “For an overviewof SPT and a discussion of relative arbitrage opportunities, we recommend the reader consult the monograph by Fernholz (2002) and the survey paper by Fernholz and Karatzas (2009).”
HYBRID ATLAS MODELS (2009, background): “largest company k =1 down to the smallest k =n. The capital distribution curve for the US equity market has shown remarkable stability over the last century (see, for instance, Figure 5.1 of Fernholz [13]), and this stability has been captured in the Atlas and ﬁrst-order Received September 2009; rev”
ONE-DIMENSIONAL BROWNIAN PARTICLE SYSTEMS WITH RANK DEPENDENT DRIFTS (2007, positive): “he directed polymer models, and the GUE random matrix ensemble. More recently rank dependent SDEs have been considered by several authors as possible models for ﬁnancial or economic data. Fernholz in [10] introduces the so-called Atlas model which we study in this paper. It is a model of ﬁnitely man”
Relative arbitrage in volatility-stabilized markets (2005, methodology): “The quantity γπ∗ (t) := 1 2 n∑ i=1 πi(t)aii(t)− n∑ i=1 n∑ j=1 πi(t)aij(t)πj(t) (2.9) is non-negative, and is strictly positive if πi(t) > 0 holds a.s. for all i = 1, · · · , n and t ≥ 0 ; see Proposition 1.3.7 in Fernholz (2002).”
On the difference between entropic cost and the optimal transport cost (2019, neutral): “See [13, 23].”
Convergence rates for rank-based models with applications to portfolio theory (2011, methodology): “() is dened as a solution to dVˇ(t) Vˇ(t) = X i2I ˇ i(t) dS i(t) S i(t) : For example, ˇ i(:) = i(:), i2Igives the market portfolio and we will write V() for its value process. Following Fernholz [17], we introduce the family Cof portfolio generating functions G : U!(0;1), which are functions of cl”
The geometry of relative arbitrage (2014, methodology): “We close the current subsection by showing in the next lemma that our definition is consistent with Fernholz’s.”
Atlas models of equity markets (2005, background): “…+ σkBk(t)(A.4) holds for every k = 1, . . . , n. Fix k ∈ {1, . . . , n − 1} and observe kZk(t) ≤ k∑ =1 Z (t) (A.5) = k∑ =1 Z (0) + ( kγ + k∑ =1 g ) t + 12 k,k+1(t) + k∑ =1 σ B (t), (n − k)Zk(t) ≥ n∑ =k+1 Z (t) = n∑ =k+1 Z (0) + ( (n − k)γ + n∑ =k+1 g ) t(A.6) − 12 k,k+1(t) + n∑ =k+1 σ B (t).”
Systems of Brownian particles with asymmetric collisions (2012, methodology): “95 of [10]), one sees that a q-Atlas model can capture the concave shape of the capital distribution curve, as well as its linear structure at the top.”