Related papers: Dynamic Limit Growth Indices in Discrete Time
The financial crisis has dramatically demonstrated that the traditional approach to apply univariate monetary risk measures to single institutions does not capture sufficiently the perilous systemic risk that is generated by the…
We study finite episodic Markov decision processes incorporating dynamic risk measures to capture risk sensitivity. To this end, we present two model-based algorithms applied to \emph{Lipschitz} dynamic risk measures, a wide range of risk…
We define and develop an approach for risk budgeting allocation - a risk diversification portfolio strategy - where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions…
This paper approaches the definition and properties of dynamic convex risk measures through the notion of a family of concave valuation operators satisfying certain simple and credible axioms. Exploring these in the simplest context of a…
The time value of money is a critical factor not only in risk analysis, but also in insurance and financial applications. In this paper, we consider a special class of set-valued risk statistics by introducing the time value of money. In…
To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…
We present a new average-based robustness score for Signal Temporal Logic (STL) and a framework for optimal control of a dynamical system under STL constraints. By averaging the scores of different specifications or subformulae at different…
In this paper, we propose two discontinuous dynamical systems in continuous time with guaranteed prescribed finite-time local convergence to strict local minima of a given cost function. Our approach consists of exploiting a Lyapunov-based…
In this paper, we consider the notions of effort and resilience of a dynamical control system defined by the maximum disturbance the system can withstand while satisfying given finite temporal logic specifications. Given a dynamical system…
The robustness of dynamical systems against external perturbations is crucial in engineering; however, it is often overlooked for the lack of methods for rapidly computing it. This paper proposes a novel algorithm for estimating the…
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…
Recently, time scales calculus is developed to unify continuous and discrete analysis. By extending the definition of time scales properly, this paper introduces the concept of a signal set as well as its stability properties in terms of…
Existing drift detection methods focus on designing sensitive test statistics. They treat the detection threshold as a fixed hyperparameter, set once to balance false alarms and late detections, and applied uniformly across all datasets and…
Evaluating robustness under temporal distribution shift remains an open challenge. Existing metrics quantify the average decline in performance, but fail to capture how models adapt to evolving data. As a result, temporal degradation is…
The continuous time model of dynamic asset trading is the central model of modern finance. Because trading cannot in fact take place at every moment of time, it would seem desirable to show that the continuous time model can be viewed as…
In this paper, we consider the notion of resilience of a dynamical system, defined by the maximum disturbance a controlled dynamical system can withstand while satisfying given temporal logic specifications. Given a dynamical system and a…
Positive linear systems on arbitrary time scales are studied. The theory developed in the paper unifies and extends concepts and results known for continuous-time and discrete-time systems. A necessary and sufficient condition for a linear…
In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of…
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…
Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…