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An improved bound for the dimension of (α, 2α)-Furstenberg sets
(2022)
We show that given α e (0, 1) there is a constant c = c α > 0 such that any planar (α, 2α)-Furstenberg set has Hausdorff dimension at least 2α + c. This improves several previous bounds, in particular extending a result ...
Farkas’ Lemma in the bilinear setting and evaluation functionals
(Real Academia de Ciencias Exactas, Físicas y Naturales, 2023)
We prove the following Farkas’ Lemma for simultaneously diagonalizable bilinear forms:
If A1, . . . , Ak, and B : Rn × Rn → R are bilinear forms, then one—and only one—of the
following holds:
(i) B = a1A1 +· · ·+ak Ak ...
Optimal Ratcheting of Dividends in a Brownian Risk Model
(2020)
We study the problem of optimal dividend payout from a surplus process governed by Brownian motion with drift under the additional constraint of ratcheting,
i.e. the dividend rate can never decrease. We solve the resulting ...
Optimal dividend strategies for a catastrophe insurer
(Frontiers of Mathematical Finance (e- ISSN:2769-6715), 2024-06)
In this paper we study the problem of optimally paying out dividends
from an insurance portfolio, when the criterion is to maximize the expected
discounted dividends over the lifetime of the company and the portfolio
contains ...
On the volume ratio of projections of convex bodies
(Universidad Torcuato Di Tella, 2022)
We study the volume ratio between projections of two convex bodies. Given
a high-dimensional convex body K we show that there is another convex body L such
that the volume ratio between any two projections of fixed rank ...