Related papers: A delayed dual risk model
We describe a situation where an unstable equilibrium in a $3 \times 3$ system of linear differential equations may be stabilized by introducing a delayed response, i.e. converting to a system of delayed differential equations. This…
We investigate an insurance risk model that consists of two reserves which receive income at fixed rates. Claims are being requested at random epochs from each reserve and the interclaim times are generally distributed. The two reserves are…
Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical, and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates…
Undulation of infection levels, usually called waves, are not well understood. In this paper we propose a mathematical model that exhibits undulation and decay towards a stable state. The model is a re-interpretation of the original…
We consider a logistic differential equation subject to impulsive delayed harvesting, where the deduction information is a function of the population size at the time of one of the previous impulses. A close connection to the dynamics of…
The mathematical - numerical analysis of a discrete dynamical model with two independent delays was performed. Such model may describe a continuous system with delays that have real rational number values. Applicable characteristic…
Motivated by interest in providing more efficient services in customer service systems, we use statistical learning methods and delay history information to predict the conditional distribution of the customers' waiting times in queueing…
In this work we introduce a differential equation model with time-delay that describes the three-stage dynamics and the two time scales observed in HIV infection. Assuming that the virus has high mutation and rapid reproduction rates that…
The risk of overparameterized models, in particular deep neural networks, is often double-descent shaped as a function of the model size. Recently, it was shown that the risk as a function of the early-stopping time can also be…
This paper investigates the second order asymptotic expansion for tail probabilities of discounted aggregate claims in continuous-time renewal risk models with constant interest force. Concretely, two types of continuous-time renewal risk…
Stochastic linear bandits are a natural and well-studied model for structured exploration/exploitation problems and are widely used in applications such as online marketing and recommendation. One of the main challenges faced by…
We study linear dueling bandits in volatile environments characterized by the simultaneous presence of post-serving contexts, delayed feedback, and adversarial corruption. Feedback is subject to unknown stochastic or adversarial delays and…
Action delays degrade the performance of reinforcement learning in many real-world systems. This paper proposes a formal definition of delay-aware Markov Decision Process and proves it can be transformed into standard MDP with augmented…
Distributed systems in which concurrent proposals are mutually exclusive face a fundamental stability constraint under network delay. In open systems where global state progression is event-driven rather than round-driven, propagation delay…
In this paper we analyze so-called Parisian ruin probability that happens when surplus process stays below zero longer than fixed amount of time $\zeta>0$. We focus on general spectrally negative L\'{e}vy insurance risk process. For this…
This paper extends the classical dividend problem by incorporating a novel, path-dependent mechanism of firm default. In the traditional framework, ruin occurs when the surplus process first reaches zero. In contrast, default in our model…
Generative models trained on finite data face a fundamental tension: their score-matching or next-token objective converges to the empirical training distribution rather than the population distribution we seek to learn. Using rule-valid…
The paper deals with a generalization of the risk model with stochastic premiums where dependence structures between claim sizes and inter-claim times as well as premium sizes and inter-premium times are modeled by…
Existing mathematical models of delay discounting (e. g. exponential model, hyperbolic model, and those derived from nonextensive statistics) consider impulsivity as a single entity. However, the present article derives a novel mathematical…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…