arXiv subjects

Radoš Radoičić

Publications and source records attributed to Radoš Radoičić.

5 recordsLinked to original sources

arXiv2026

Insertion and expansion of cylinders around the unit ball

A unit ball is surrounded with a ring of $n$ equal infinite circular cylinders. Each cylinder touches the ball and its two neighbors. Can one more cylinder of the same radius be added if the configuration may be rearranged? Can the $n$ cylinders instead be enlarged, and by how much? We prove that insertion is impossible for $3\le n\le7$ and possible for $n\ge9$. The case $n=8$ remains open. The case $n=6$ is Kuperberg's problem from 1990, which was resolved recently. We prove that the ring of four cylinders cannot be expanded. This settles a conjecture of Ogievetsky and Shlosman from 2018. For $n\ge5$ the largest possible expansion radius remains unknown.

math.MG↗

arXiv2024

A generalization of the rational rough Heston approximation

Previously, in [GR19], we derived a rational approximation of the solution of the rough Heston fractional ODE in the special case λ= 0, which corresponds to a pure power-law kernel. In this paper we extend this solution to the general case of the Mittag-Leffler kernel with λ\geq 0. We provide numerical evidence of the convergence of the solution.

q-fin.CP↗

arXiv2020

Forests, cumulants, martingales

This work is concerned with forest and cumulant type expansions of general random variables on a filtered probability spaces. We establish a "broken exponential martingale" expansion that generalizes and unifies the exponentiation result of Al{ò}s, Gatheral, and Radoičić and the cumulant recursion formula of Lacoin, Rhodes, and Vargas. Specifically, we exhibit the two previous results as lower dimensional projections of the same generalized forest expansion, subsequently related by forest reordering. Our approach also leads to sharp integrability conditions for validity of the cumulant formula, as required by many of our examples, including iterated stochastic integrals, Lévy area, Bessel processes, KPZ with smooth noise, Wiener-Itô chaos and "rough" stochastic (forward) variance models.

math.PR↗

arXiv2018

The Zumbach effect under rough Heston

Previous literature has identified an effect, dubbed the Zumbach effect, that is nonzero empirically but conjectured to be zero in any conventional stochastic volatility model. Essentially this effect corresponds to the property that past squared returns forecast future volatilities better than past volatilities forecast future squared returns. We provide explicit computations of the Zumbach effect under rough Heston and show that they are consistent with empirical estimates. In agreement with previous conjectures however, the Zumbach effect is found to be negligible in the classical Heston model.

q-fin.ST↗

arXiv2014

Saturated simple and $k$-simple topological graphs

A simple topological graph $G$ is a graph drawn in the plane so that any pair of edges have at most one point in common, which is either an endpoint or a proper crossing. $G$ is called saturated if no further edge can be added without violating this condition. We construct saturated simple topological graphs with $n$ vertices and $O(n)$ edges. For every $k>1$, we give similar constructions for $k$-simple topological graphs, that is, for graphs drawn in the plane so that any two edges have at most $k$ points in common. We show that in any $k$-simple topological graph, any two independent vertices can be connected by a curve that crosses each of the original edges at most $2k$ times. Another construction shows that the bound $2k$ cannot be improved. Several other related problems are also considered.

math.CO↗