Related papers: Conditional Value at Risk and Partial Moments for …
We introduce a semiparametric approach for forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) by modeling the conditional scale of financial returns, defined as the difference between two specified quantiles, via restricted…
Set-valued risk measures on $L^p_d$ with $0 \leq p \leq \infty$ for conical market models are defined, primal and dual representation results are given. The collection of initial endowments which allow to super-hedge a multivariate claim…
We present a new temporal logic called Distribution Temporal Logic (DTL) defined over predicates of belief states and hidden states of partially observable systems. DTL can express properties involving uncertainty and likelihood that cannot…
Conditional expectation \mathbb{E}(Y \mid X) often fails to capture the complexity of multimodal conditional distributions \mathcal{L}(Y \mid X). To address this, we propose using n-point conditional quantizations--functional mappings of X…
The concept of univariate Range Value-at-Risk, presented by Cont et al. (2010), is extended in the multidimensional setting. Traditional risk measures are not well suited when dealing with heavy-tail distributions and infinite tail…
A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of distribution which determines the dependency between one…
Based on supermodularity ordering properties, we show that convex risk measures of credit losses are nondecreasing w.r.t. credit-credit and, in a wrong-way risk setup, credit-market, covariances of elliptically distributed latent factors.…
Capital allocation is a procedure used to assess the risk contributions of individual risk components to the total risk of a portfolio. While the conditional tail expectation (CTE)-based capital allocation is arguably the most popular…
We analyze systems of agents sharing light-tailed risky claims issued by different financial objects. Assuming exponentially distributed claims, we obtain that both agents' and system's losses follow generalized exponential mixture…
In this paper we define the class of matrix Mittag-Leffler distributions and study some of its properties. We show that it can be interpreted as a particular case of an inhomogeneous phase-type distribution with random scaling factor, and…
This paper develops a safety analysis method for stochastic systems that is sensitive to the possibility and severity of rare harmful outcomes. We define risk-sensitive safe sets as sub-level sets of the solution to a non-standard optimal…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…
Working in a continuous time setting, we extend to the general case of dynamic risk measures continuous from above the characterization of time consistency in terms of ``cocycle condition'' of the minimal penalty function. We prove also the…
Given the high volatility and susceptibility to extreme events in the cryptocurrency market, forecasting tail risk is of paramount importance. Value-at-Risk (VaR), a quantile-based risk measure, is widely used for assessing tail risk and is…
We provide a constructive way of defining new elicitable risk measures that are characterised by a multiplicative scoring function. We show that depending on the choice of the scoring function's components, the resulting risk measure…
We study the aggregation of two risks when the marginal distributions are known and the dependence structure is unknown, under the additional constraint that one risk is smaller than or equal to the other. Risk aggregation problems with the…
In this paper, we consider a property of univariate Gaussian distributions namely conditional expectation shift (or centroid shift). Specifically, we compare two Gaussian distributions in which they differ only in their means. Equivalently,…
Inflation exhibits state-dependent, skewed, and fat-tailed dynamics that make risk a central concern for monetary policy. Accordingly, inflation risks are distributional and cannot be fully captured by mean-based models. We propose a…
Risk management is very important for individual investors or companies. There are many ways to measure the risk of investment. Prices of risky assets vary rapidly and randomly due to the complexity of finance market. Random interval is a…