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This article constructs a forward exponential utility in a market with multiple defaultable risks. Using the Jacod-Pham decomposition for random fields, we first characterize forward performance processes in a defaultable market under the…
We study an open problem of risk-sensitive portfolio allocation in a regime-switching credit market with default contagion. The state space of the Markovian regime-switching process is assumed to be a countably infinite set. To characterize…
The problem of vanishing and exploding gradients has been a long-standing obstacle that hinders the effective training of neural networks. Despite various tricks and techniques that have been employed to alleviate the problem in practice,…
We investigate the KNO scaling function of the modified negative binomial distribution (MNBD), because this MNBD can explain the oscillating behaviors of the cumulant moment observed in $e^+e^-$ annihilations and in hadronic collisions. By…
In this work, we study the binary neural networks (BNNs) of which both the weights and activations are binary (i.e., 1-bit representation). Feature representation is critical for deep neural networks, while in BNNs, the features only differ…
Spiking Neural Networks (SNNs) are energy-efficient and biologically plausible, ideal for embedded and security-critical systems, yet their adversarial robustness remains open. Existing adversarial attacks often overlook SNNs' bio-plausible…
The full statistical distribution of the superfluid fraction characterizing one-dimensional Bose gases in random potentials is discussed. Rare configurations with extreme fluctuations of the disorder potential can fragment the condensate…
This paper analyzes the effects of input uncertainties on the outputs of a three dimensional natural convection problem in a differentially heated cubical enclosure. Two different cases are considered for parameter uncertainty propagation…
Option pricing in real markets faces fundamental challenges. The Black--Scholes--Merton (BSM) model assumes constant volatility and uses a linear generator $g(t,x,y,z)=-ry$, while lacking explicit behavioral factors, resulting in systematic…
We introduce squared neural Poisson point processes (SNEPPPs) by parameterising the intensity function by the squared norm of a two layer neural network. When the hidden layer is fixed and the second layer has a single neuron, our approach…
Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects we devise an analytically solvable model…
Modelling systems with networks has been a powerful approach to tame the complexity of several phenomena. Unfortunately, such an approach is often made difficult by the large number of variables to take into consideration. Methods of…
The tail of a bivariate distribution function in the domain of attraction of a bivariate extreme-value distribution may be approximated by the one of its extreme-value attractor. The extreme-value attractor has margins that belong to a…
A new class of nonparametric prior distributions, termed Beta-Binomial stick-breaking process, is proposed. By allowing the underlying length random variables to be dependent through a Beta marginals Markov chain, an appealing discrete…
We focus on the development of diagnostic tools and an R package called MNB for a multivariate negative binomial (MNB) regression model for detecting atypical and influential subjects. The MNB model is deduced from a Poisson mixed model in…
We propose a tractable semiparametric estimation method for structural dynamic discrete choice models. The distribution of additive utility shocks in the proposed framework is modeled by location-scale mixtures of extreme value…
Multiplicity distributions $P(N)$ measured in multiparticle production processes are most frequently described by the Negative Binomial Distribution (NBD). However, with increasing collision energy some systematic discrepancies become more…
The Bak-Tang-Wiesenfeld (BTW) sandpile process is an archetypal, stylized model of complex systems with a critical point as an attractor of their dynamics. This phenomenon, called self-organized criticality (SOC), appears to occur…
We study an optimal investment/consumption problem in a model capturing market and credit risk dependencies. Stochastic factors drive both the default intensity and the volatility of the stocks in the portfolio. We use the martingale…
We define a family of probability distributions for random count matrices with a potentially unbounded number of rows and columns. The three distributions we consider are derived from the gamma-Poisson, gamma-negative binomial, and…