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We propose a novel framework for Network Stochastic Differential Equations (N-SDE), where each node in a network is governed by an SDE influenced by interactions with its neighbors. The evolution of each node is driven by the interplay of…
Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The…
This paper expands traditional stochastic volatility models by allowing for time-varying skewness without imposing it. While dynamic asymmetry may capture the likely direction of future asset returns, it comes at the risk of leading to…
We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence structure is modeled via Archimedean…
We consider a class of semi-linear differential Volterra equations with memory terms, polynomial nonlinearities and random perturbation. For a broad class of nonlinearities, we study statistically steady states of the system and find that…
Currency crises are frequently discussed retrospectively as a necessary and deterministic outcome of a finite sequence of fiscal decisions, monetary manoeuvres, and limited exogenous inputs. Parallelly, the Twin Deficits Hypothesis (TDH)…
We investigate model risk and distributionally robust optimization (DRO) under marginal and martingale constraints. Building on our previous work, we address the previously open case of static hedging with second-period maturity vanilla…
Stochastic epidemic models provide an interpretable probabilistic description of the spread of a disease through a population. Yet, fitting these models to partially observed data is a notoriously difficult task due to intractability of the…
We introduce a response-theoretic framework that recasts parameter calibration of ergodic stochastic differential equations as a fluctuation-dissipation problem. Our central result is that the full Jacobian of any stationary observable with…
We present a family of models for the term structure of interest rates which describe the interest rate curve as a stochastic process in a Hilbert space. We start by decomposing the deformations of the term structure into the variations of…
We develop a model-theoretic framework for the study of distal factors of strongly ergodic, measure-preserving dynamical systems of countable groups. Our main result is that all such factors are contained in the (existential) algebraic…
For a Markov decision process with countably infinite states, the optimal value may not be achievable in the set of stationary policies. In this paper, we study the existence conditions of an optimal stationary policy in a countable-state…
We introduce a prototype agent-based model of the macroeconomy, with budgetary constraints at its core. The model is related to a class of constraint satisfaction problems (CSPs), which has been thoroughly investigated in computer science.…
We present an arbitrage free theoretical framework for modeling bid and ask prices of dividend paying securities in a discrete time setup using theory of dynamic acceptability indices. In the first part of the paper we develop the theory of…
Linear response theory, the backbone of non-equilibrium statistical physics, has recently been extended to explain how and why non-ergodic renewal processes are insensitive to simple perturbations, such as in habituation. It was established…
This work introduces a new framework for modeling financial markets through an interpretable probabilistic state machine. By clustering historical returns based on momentum and risk features across multiple time horizons, we identify…
We provide two methodological insights on \emph{ex ante} policy evaluation for macro models of economic development. First, we show that the problems of parameter instability and lack of behavioral constancy can be overcome by considering…
In this paper, it is shown that a simple formulation of Economic Model Predictive Control can be used which possesses two features that are generally viewed as mutually exclusive, namely, a rather short prediction horizon…
The proliferation of intermittent distributed renewable energy sources (RES) in modern power systems has fundamentally compromised the reliability and accuracy of deterministic net load forecasting. Generative models, particularly diffusion…
We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, It\^{o}-process models of financial markets with random ergodic coefficients. Including {\em value-at-risk}…