arXiv subjects

Alexander Dimitrov

Publications and source records attributed to Alexander Dimitrov.

3 recordsLinked to original sources

arXiv2026

Optimal investment under capital gains taxes

We generalize classical results on the existence of optimal portfolios in discrete time frictionless market models to models with capital gains taxes. We consider the realistic but mathematically challenging rule that losses do not trigger negative taxes but can only be offset against potential gains in the future. Central to the analysis is a well-known phenomenon from arbitrage-free markets with proportional transaction costs that does not exist in arbitrage-free frictionless markets: an investment in specific quantities of stocks that is completely riskless but may provide an advantage over holding money in the bank account. As a result of this phenomenon, on an infinite probability space, no-arbitrage does not imply that the set of attainable terminal wealth is closed in probability. We show closedness under the slightly stronger {\em no unbounded non-substitutable investment with bounded risk} condition. As a by-product, we provide a proof that in discrete time frictionless models with short-selling constraints, no-arbitrage implies that the set of attainable terminal wealth is closed in probability -- even if there are redundant stocks.

q-fin.MF↗

arXiv2022

The Lack of Convexity of the Relevance-Compression Function

In this paper we investigate the convexity of the relevance-compression function for the Information Bottleneck and the Information Distortion problems. This curve is an analog of the rate-distortion curve, which is convex. In the problems we discuss in this paper, the distortion function is not a linear function of the quantizer, and the relevance-compression function is not necessarily convex (concave), but can change its convexity. We relate this phenomena with existence of first order phase transitions in the corresponding Lagrangian as a function of the annealing parameter.

cs.IT↗

arXiv2021

Mapping and Validating a Point Neuron Model on Intel's Neuromorphic Hardware Loihi

Neuromorphic hardware is based on emulating the natural biological structure of the brain. Since its computational model is similar to standard neural models, it could serve as a computational acceleration for research projects in the field of neuroscience and artificial intelligence, including biomedical applications. However, in order to exploit this new generation of computer chips, rigorous simulation and consequent validation of brain-based experimental data is imperative. In this work, we investigate the potential of Intel's fifth generation neuromorphic chip - `Loihi', which is based on the novel idea of Spiking Neural Networks (SNNs) emulating the neurons in the brain. The work is implemented in context of simulating the Leaky Integrate and Fire (LIF) models based on the mouse primary visual cortex matched to a rich data set of anatomical, physiological and behavioral constraints. Simulations on the classical hardware serve as the validation platform for the neuromorphic implementation. We find that Loihi replicates classical simulations very efficiently and scales notably well in terms of both time and energy performance as the networks get larger.

cs.NE↗