Fractional trading has emerged as an opportunity for investors to invest in fractions of shares, enabling access to high-priced stocks even with small budgets, and thus reaching a bigger investment community. Aside from the inventory risk faced by all market makers, providers of fractional trading are unable to perfectly hedge their positions and therefore need to forecast retail investors’ order flow over short time horizons to manage their market risk. We develop machine learning models to predict trading activity in fractional trading using time series data on investor holdings of a large set of securities across different sectors combined with daily news sentiment indicators. Our approach proceeds in two stages. First, securities are grouped into clusters with similar trading patterns, and representative firms are selected from each cluster. Second, trading activity is modeled using long short-term memory (LSTM) neural networks augmented with sentiment features. The results show that fractional trading activity can be modeled with meaningful predictive accuracy and that incorporating news sentiment improves LSTM performance in most cases. In two stylised examples, we demonstrate approaches to hedging and market risk management using the LSTM predictions. Feature importance analysis using methods from explainable artificial intelligence (XAI) identifies the primary drivers of trading activity.
This paper addresses the maintenance optimization of a parallel system comprising two components subject to stochastically dependent degradation processes. The focus is placed on the scenario of partial observability, where the condition of only one component is observed/observable. The degradation of the components is described using a bivariate gamma process with random effect. The dependence is modeled assuming that the two components share the same random effect. The failure time distribution and the predictive distribution of the unobserved component are derived. A maintenance policy based on a single inspection within a finite time horizon is also formulated. At the inspection time, four actions are possible: do nothing, replace either component, or replace both. Decisions are made by using a non-parametric condition-based decision rule informed by the observed degradation level. The system is assumed to operate over a finite time horizon. The optimal policy is obtained by minimizing the expected maintenance cost, incorporating preventive and corrective costs as well as downtime and inspection costs. The optimal policy is determined by using a numerical approach, showing that information from the observable component enables effective maintenance decisions for the whole system even when the degradation of the other component is completely hidden. For the sake of comparison, the proposed maintenance policy is extended to the case where the inspection involves both components. Although it is not the main goal of the study, this latter result represents an additional (minor) contribution of the paper.
This paper develops a Bernstein polynomial estimator for binomial regression under a balanced, equispaced fixed design. Explicit asymptotic expansions are derived for the bias, variance, mean squared error, and mean integrated squared error. Under suitable regularity conditions, we establish asymptotic normality of the centered estimator at interior points together with a quantitative Berry–Esseen bound. We further derive the asymptotic normality of an associated integral statistic, thereby complementing the pointwise theory with a global distributional result. Corresponding distributional results for fixed degrees are also presented. Simulations illustrate boundary and integrated accuracy relative to the Nadaraya–Watson estimator and examine the theoretical normal approximation.
This paper is concerned with the study of the system reliability under a delta shock model when the intershock times follow a certain kind of dependence. In particular, exact equations are obtained for the reliability and mean time to failure of the system when the times between shocks follow discrete autoregressive process of order 1. Extensive numerical examples are presented for various intershock time distributions such geometric, negative binomial and phase-type. The impact of dependency on system reliability and mean time to failure is analyzed by comparing it numerically to the case of independence. The model is further extended to a mixed shock setting in which the system may also fail due to a large shock magnitude. In this extension, both the intershock times and the shock magnitudes follow discrete autoregressive processes of order 1, so that serial dependence is present on both sides. Exact expressions are obtained for the probability mass function and the mean time to failure of the lifetime under the mixed model. Numerical results illustrate the joint effect of the two dependence parameters on the reliability of the system.
This paper investigates a single-server queueing system characterized by a rating-dependent correlated arrival process and unreliable service. The service process follows a Phase-Type distribution with failures. In the event of a failure, a customer may be lost, re-serviced from the beginning, or resumed from the interrupted phase. Customers in the infinite-capacity buffer exhibit impatience and may renege. The system’s rating, which directly influences the arrival rate, fluctuates according to specific probabilities triggered by arrivals, service completions, or reneging events. When the rating hits the minimum threshold, a promotion is issued to increase it by a fixed increment. We model the system behavior as a continuous-time Markov chain and establish the ergodicity conditions for both patient and impatient customer cases. We develop an efficient algorithm for computing the steady-state distribution and derive a comprehensive set of performance metrics. Furthermore, the Laplace-Stieltjes transforms of distributions of the customer’s sojourn time and waiting time are analyzed. The possibility of cost criterion optimization through the strategic selection of the promotion increment is demonstrated.
