Related papers: Dynamic risk measures
A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often…
In Willems' behavioral systems theory, a dynamical system is identified with the set of all trajectories compatible with its laws of motion. In the linear time-invariant setting this trajectory set is a linear subspace, and its algebraic…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…
In this paper we present results on scalar risk measures in markets with transaction costs. Such risk measures are defined as the minimal capital requirements in the cash asset. First, some results are provided on the dual representation of…
This article shows how to specify and construct a discrete, stochastic, continuous-time model specifically for ecological systems. The model is more broad than typical chemical kinetics models in two ways. First, using time-dependent hazard…
This paper investigates the optimization problem of an infinite stage discrete time Markov decision process (MDP) with a long-run average metric considering both mean and variance of rewards together. Such performance metric is important…
Risk measures like Marginal Expected Shortfall and Marginal Mean Excess quantify conditional risk and in particular, aid in the understanding of systemic risk. In many such scenarios, models exhibiting heavy tails in the margins and…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
In this paper we present results on dynamic multivariate scalar risk measures, which arise in markets with transaction costs and systemic risk. Dual representations of such risk measures are presented. These are then used to obtain the main…
Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are…
We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk…
We introduce set risk measures (SRMs), real-valued maps defined on the family of non-empty closed bounded sets of essentially bounded random variables. SRMs extend traditional scalar risk measures by assigning a single capital requirement…
In this paper we derive robust super- and subhedging dualities for contingent claims that can depend on several underlying assets. In addition to strict super- and subhedging, we also consider relaxed versions which, instead of eliminating…
This paper provides new conditions for dynamic optimality in discrete time and uses them to establish fundamental dynamic programming results for several commonly used recursive preference specifications. These include Epstein-Zin…
In a dynamic framework, we identify a new concept associated with the risk of assessing the financial exposure by a measure that is not adequate to the actual time horizon of the position. This will be called horizon risk. We clarify that…
We consider optimal control problems for diffusion processes, where the objective functional is defined by a time-consistent dynamic risk measure. We focus on coherent risk measures defined by $g$-evaluations. For such problems, we…