相关论文: Risk Forms: Representation, Disintegration, and Ap…

We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…

This note describes the functional-integral quantization of two-dimensional topological field theories together with applications to problems in deformation quantization of Poisson manifolds and reduction of certain submanifolds. A brief…

We propose a route for the evaluation of risk based on a transformation of the covariance matrix. The approach uses a `potential' or `objective' function. This allows us to rescale data from different assets (or sources) such that each data…

Inspired by widely-used techniques of causal modelling in risk, failure, and accident analysis, this work discusses a compositional framework for risk modelling. Risk models capture fragments of the space of risky events likely to occur…

We introduce a distributional method for learning the optimal policy in risk averse Markov decision process with finite state action spaces, latent costs, and stationary dynamics. We assume sequential observations of states, actions, and…

The Minkowski question mark function is a rich object which can be explored from the perspective of dynamical systems, complex dynamics, metric number theory, multifractal analysis, transfer operators, integral transforms, and as a function…

We propose a method to assess the intrinsic risk carried by a financial position $X$ when the agent faces uncertainty about the pricing rule assigning its present value. Our approach is inspired by a new interpretation of the quasiconvex…

We consider a large class of physical fields $u$ written as double inverse Fourier transforms of some functions $F$ of two complex variables. Such integrals occur very often in practice, especially in diffraction theory. Our aim is to…

We introduce a formal notion of masking fault-tolerance between probabilistic transition systems based on a variant of probabilistic bisimulation (named masking simulation). We also provide the corresponding probabilistic game…

We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by…

A measure representation result for a functional modelling optimal design problems for plastic deformations, under linear growth conditions, is obtained. Departing from an energy with a bulk term depending on the deformation gradient and…

Conditioning, the central operation in Bayesian statistics, is formalised by the notion of disintegration of measures. However, due to the implicit nature of their definition, constructing disintegrations is often difficult. A folklore…

Data refinement is the standard extension of a refinement relation from programs to datatypes (i.e. a behavioural subtyping relation). Forward/backward simulations provide a tractable method for establishing data refinement, and have been…

In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($\Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes…

We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…

Risk measures connect probability theory or statistics to optimization, particularly to convex optimization. They are nowadays standard in applications of finance and in insurance involving risk aversion. This paper investigates a wide…

This paper develops a two-step estimation methodology, which allows us to apply catastrophe theory to stock market returns with time-varying volatility and model stock market crashes. Utilizing high frequency data, we estimate the daily…

Methods for causal inference are well developed for binary and continuous exposures, but in many settings, the exposure has a substantial mass at zero-such exposures are called semi-continuous. We propose a general causal framework for such…

The analysis and control of stochastic dynamical systems rely on probabilistic models such as (continuous-space) Markov decision processes, but large or continuous state spaces make exact analysis intractable and call for principled…

This paper is concerned with a characterization of the observability for a continuous-time hidden Markov model where the state evolves as a general continuous-time Markov process and the observation process is modeled as nonlinear function…