相关论文: On Quantile Risk Measures and Their Domain

In this paper, we consider a situation where a decision maker's (DM's) risk preference can be described by a spectral risk measure (SRM) but there is not a single SRM which can be used to represent the DM's preferences consistently.…

The most basic scenario of quantum control involves the organized manipulation of pure dynamical states of the system by means of unitary transformations. Recently, Vilela Mendes and Mank'o have shown that the conditions for controllability…

Probabilistic metrology attempts to improve parameter estimation by occasionally reporting an excellent estimate and the rest of the time either guessing or doing nothing at all. Here we show that probabilistic metrology can never improve…

This paper introduces a new framework for multivariate quantile regression based on the multivariate distribution function, termed multivariate quantile regression (MQR). In contrast to existing approaches--such as directional quantiles,…

Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the…

In Quantum Non Demolition measurements, the sequence of observations is distributed as a mixture of multinomial random variables. Parameters of the dynamics are naturally encoded into this family of distributions. We show the local…

The structure of a local hidden variable model for experiments involving sequences of measurements rigorously is analyzed. Constraints imposed by local realism on the conditional probabilities of the outcomes of such measurement schemes are…

We obtain the uniform measure as a stationary measure of the one-dimensional discrete-time quantum walks by solving the corresponding eigenvalue problem. As an application, the uniform probability measure on a finite interval at a time can…

It is well-known in quantum information theory that a positive operator valued measure (POVM) is the most general kind of quantum measurement. Mathematically, a quantum probability is a normalised POVM, namely a function on certain subsets…

This paper introduces a qualitative measure of ambiguity and analyses its relationship with other measures of uncertainty. Probability measures relative likelihoods, while ambiguity measures vagueness surrounding those judgments. Ambiguity…

Quantum metrology uses small changes in the output probabilities of a quantum measurement to estimate the magnitude of a weak interaction with the system. The sensitivity of this procedure depends on the relation between the input state,…

The classical concept of inequality curves and measures is extended to conditional inequality curves and measures and a curve of conditional inequality measures is introduced. This extension provides a more nuanced analysis of inequality in…

We develop a novel stochastic valuation and premium calculation principle based on probability measure distortions that are induced by quantile processes in continuous time. Necessary and sufficient conditions are derived under which the…

It is proposed to define "quantumness" of a system (micro or macroscopic, physical, biological, social, political) by starting with understanding that quantum mechanics is a statistical theory. It says us only about probability…

Quantum measurement is a fundamental cornerstone of experimental quantum computations. The main issues in current quantum measurement strategies are the high number of measurement rounds to determine a global optimal measurement output and…

Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify…

Quantile regression is an effective technique to quantify uncertainty, fit challenging underlying distributions, and often provide full probabilistic predictions through joint learnings over multiple quantile levels. A common drawback of…

Multi-period measures of risk account for the path that the value of an investment portfolio takes. In the context of probabilistic risk measures, the focus has traditionally been on the magnitude of investment loss and not on the dimension…

Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric…

Risk measures are important key figures to measure the adequacy of the reserves of a company. The most common risk measures in practice are Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). Recently, quantum-based algorithms are…