A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study on risk measures using distorted Choquet integrals with random distortions.
problem Developing risk measures under random distortions of capacities.
method Introducing and analyzing randomly distorted Choquet integrals with respect to a distorted capacity, establishing properties and providing representations.
result Representation of comonotonic additive conditional risk measures using G-randomly distorted Choquet integrals.
We discuss equivalent axiomatic characterizations of distortion risk measures, and give a novel and concise proof of the characterization of elicitable distortion risk measures. Elicitability has recently been discussed as a desirable criterion for risk measures, motivated by statistical considerations of forecasting. …
Study dynamic risk measures and performance indices using distortion functions.
problem Investigate time consistency of dynamic risk measures and performance indices generated by distortion functions.
method Analyze dynamic coherent risk measures (DCRMs) and dynamic weighted value at risk measures, proving their equivalence. Establish properties of families of DCRMs generated by distortion functions and define corresponding dynamic coherent acceptability indices (DCAIs). Examine time consistency of DCRMs and DCAIs.
result DCRM generated by distortion functions are sub-martingale time consistent but not super-martingale time consistent and not weakly acceptance time consistent.
We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The second, simultaneously applies the distortion on the survival function of the su…
Study risk sharing among agents with varying risk preferences.
problem Risk sharing among agents with heterogeneous risk measures.
method Derive explicit solutions for inf-convolution and counter-monotonic inf-convolution under varying risk seeking.
result Explicit solutions for inf-convolution and counter-monotonic inf-convolution can be represented by a generalization of distortion risk measures.
Distortion risk measures are extensively used in finance and insurance applications because of their appealing properties. We present three methods to construct new class of distortion functions and measures. The approach involves the composting methods, the mixing methods and the approach that based on the theory of c…
New method for risk quantification using quantile processes and measure distortions.
problem Risk quantification and valuation in financial markets.
method Develops a novel stochastic valuation principle based on probability measure distortions induced by quantile processes.
result Introduces a system of subjective probability measures that indexes a stochastic valuation principle susceptible to probability measure distortions.
In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution (ΔCoD) measures as measures of systemic risk and analyze their properties and representations. The classes include the well-known conditional Value-at-Risk, conditional Expected Shortfall, and r…
The paper studies risk-sharing allocations for risk-seeking agents using a common distortion risk measure.
problem Characterizing Pareto-optimal risk-sharing allocations for risk-seeking agents.
method Modeling preferences with a common distortion risk measure and analyzing three settings: risk-averse, risk-seeking, and inverse S-shaped distortion.
result Pareto-optimal allocations for risk-seeking agents are counter-monotonic, not comonotonic.
In this paper, we consider the problem of optimal reinsurance design, when the risk is measured by a distortion risk measure and the premium is given by a distortion risk premium. First, we show how the optimal reinsurance design for the ceding company, the reinsurance company and the social planner can be formulated i…
Under Solvency II the computation of capital requirements is based on value at risk (V@R). V@R is a quantile-based risk measure and neglects extreme risks in the tail. V@R belongs to the family of distortion risk measures. A serious deficiency of V@R is that firms can hide their total downside risk in corporate network…
We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic dominance (and beyond). Such a family is especially suitable for representing a …
The paper calculates bounds for risk metrics and entropies under partial information constraints.
problem Analyzing risk metrics and entropies for unimodal, symmetric distributions with limited information.
method Develops lower and upper bounds for worst-case distortion riskmetrics and weighted entropy for unimodal, symmetric distributions with known mean and variance.
result Sharp upper bounds for distortion riskmetrics and weighted entropy for symmetric distributions.
The aims of this study are twofold. First, we consider an optimal risk allocation problem with non-convex preferences. By establishing an infimal representation for distortion risk measures, we give some necessary and sufficient conditions for the existence of optimal and asymptotic optimal allocations. We will show th…
Distortion (Denneberg 1990) is a well known premium calculation principle for insurance contracts. In this paper, we study sensitivity properties of distortion functionals w.r.t. the assumptions for risk aversion as well as robustness w.r.t. ambiguity of the loss distribution. Ambiguity is measured by the Wasserstein d…
We present an information-theoretic framework for bounding the number of labeled samples needed to train a classifier in a parametric Bayesian setting. We derive bounds on the average Lp distance between the learned classifier and the true maximum a posteriori classifier, which are well-established surrogates for th…
We characterize when a convex risk measure associated to a law-invariant acceptance set in L∞ can be extended to Lp, 1≤p<∞, preserving finiteness and continuity. This problem is strongly connected to the statistical robustness of the corresponding risk measures. Special attention is paid to concre…