arXiv subjects

El Mehdi Ainasse

Publications and source records attributed to El Mehdi Ainasse.

4 recordsLinked to original sources

arXiv2026

Topological Risk Parity

We develop \emph{Topological Risk Parity} (TRP), a tree-based portfolio construction approach intended for long/short, market neutral, factor-aware portfolios. The method is motivated by the dominance of passive/factor flows that naturally create a tree-like structure in markets. We introduce two implementation variants: (i) a rooted minimum-spanning-tree allocator, and (ii) a market/sector-anchored variant referred to here as \emph{Semi-Supervised TRP}, which imposes SPY as the root node and the 11 sector ETFs as the second layer. In both cases, the key object is a sparse rooted topology extracted from a correlation-distance graph, together with a propagation law that maps signed signals into portfolio weights. Relative to classical Hierarchical Risk Parity (HRP), TRP is non-binary and designed for signed cross-sectional signals and hedged long-short portfolios: it preserves signal direction while using return-dependence geometry to shape exposures. It accounts for the fact that there is imperfect correlation between parent and child nodes, and thus does not propagate weights entirely to the children. We can also impose economically motivated hierarchy that involves industries, sub-industries or factors, etc. This makes it much more robust to macroeconomic shocks and crises, where within-cluster correlations might spike. These features make TRP well suited for market-neutral, equity stat-arb or L/S trend-type strategies, where enforcing neutrality or limiting exposures at the market, sector or factor level is extremely important.

q-fin.PM↗

arXiv2024

High-Frequency Volatility Estimation with Fast Multiple Change Points Detection

We propose a method for constructing sparse high-frequency volatility estimators that are robust against change points in the spot volatility process. The estimators we propose are $\ell_1$-regularized versions of existing volatility estimators. We focus on power variation estimators as they represent a fundamental class of volatility estimators. We establish consistency of these estimators for the true unobserved volatility and the change points locations, showing that minimax rates can be achieved for particular volatility estimators. The new estimators utilize the computationally efficient least angle regression algorithm for estimation purposes, followed by a reduced dynamic programming step to refine the final number of change points. In terms of numerical performance, these estimators are not only computationally fast but also accurately identify breakpoints near the end of the sample, both features highly desirable in today's electronic trading environment. In terms of out-of-sample volatility prediction, our new estimators provide more realistic and smoother volatility forecasts, outperforming a broad range of classical and recent volatility estimators across various frequencies and forecasting horizons.

q-fin.ST↗

arXiv2021

Twisted Nakano-Positivity of Fields of Hilbert Spaces

In a previous article (arXiv:2111.03143), we generalized Berndtsson's Nakano-positivity by retaining the same consequences under weaker hypotheses. In this article, we propose to further generalize our "twisted" Nakano-positivity theorem to fields of Hilbert spaces associated to possibly unbounded Stein manifolds. We achieve this result using exhaustion arguments. As direct applications, we prove $\log$-plurisubharmonic variation results for a certain class of non-trivial families of Stein manifolds.

math.CV↗

arXiv2021

A Twisted Complex Brunn-Minkowski Theorem

In his Annals of Mathematics paper (2009), Berndtsson proves an important result on the Nakano positivity of holomorphic infinite-rank vector bundles whose fibers are Hilbert spaces consisting of holomorphic $L^2$-functions with respect to a family of weight functions $\left\{e^{-φ(\cdot,t)}\right\}_{t \in U}$, varying in $t \in U \in \mathbb{C}^m$, over a pseudoconvex domain. Using a variant of Hörmander's theorem due to Donnelly and Fefferman, we show that Berndtsson's Nakano positivity result holds under different (in fact, more general) curvature assumptions. This is of particular interest when the manifold admits a negative non-constant plurisubharmonic function, as these curvature assumptions then allow for some curvature negativity. We describe this setting as a "twisted" setting

math.CV↗