Comonotonic allocations are restored under certain constraints, improving risk-sharing.
problem Feasibility constraints can distort optimal risk-sharing allocations.
method Identified componentwise convex-order solidity as a sufficient condition to restore comonotonic allocations.
result Componentwise convex-order solidity ensures comonotonic improvements under feasible constraints.
Study dynamic Pareto-optimal allocations in multi-period economies with time-consistent risk measures.
problem Optimal allocation in multi-period pure-exchange economies with stochastic endowments and time-consistent risk measures.
method Introduced dynamic Pareto-optimal allocation processes and derived recursive and comonotone improvement theorems.
result Dynamic Pareto-optimal allocation processes can be constructed recursively and are comonotone.
The paper addresses risk sharing and variability measures among agents with general risk preferences.
problem Risk sharing and variability measures among agents with general risk preferences.
method Characterizes Pareto-optimal allocations using Gini deviation, mean-median deviation, and inter-quantile difference as variability measures.
result Optimal allocations are not comonotonic and feature a mixture of pairwise counter-monotonic structures.
Optimal risk sharing found for heterogeneous risk attitudes using distortion risk measures.
problem Risk sharing in economies with diverse risk attitudes.
method Modeling preferences with distortion risk measures, using comonotonic and counter-monotonic principles.
result Optimal risk sharing strategies identified based on risk attitudes, reducing the n-agent problem to a two-agent formulation. Study finds risk sharing without convexity assumptions.
problem Finding fair risk allocations among agents with heterogeneous beliefs.
method Combines local comonotone improvement with Dieudonné-type argument.
result Existence of Pareto optima without convexity assumption.
Paper provides new bounds for risk aggregation and sharing.
problem Quantitative risk management and robust risk aggregation with dependence uncertainty.
method Established new inequality for RVaR, derived extended convolution bounds, and analyzed risk sharing for averaged quantiles.
result Extended convolution bounds for robust risk aggregation and risk sharing, providing sharpness conditions and explicit expressions.
New concept of partial comonotonicity connects riskmetrics and dependence.
problem Understanding and quantifying risk metrics under partial comonotonicity.
method Developed a new notion of partial comonotonicity and established its connection to distortion riskmetrics.
result Partial comonotonicity uniquely characterizes a class of distortion riskmetrics through additivity.
Study on efficiency in economies with risk-averse agents, finding Pareto optima.
problem Efficiency in economies with risk-averse agents.
method Analysis of utility functionals, existence and characterization of Pareto optima.
result Existence and comonotone characterization of Pareto optima for risk-averse agents.
The classical notion of comonotonicity has played a pivotal role when solving diverse problems in economics, finance, and insurance. In various practical problems, however, this notion of extreme positive dependence structure is overly restrictive and sometimes unrealistic. In the present paper, we put forward a notion…
Simple conditions for comonotonic additive risk measures from acceptance sets.
problem Conditions for comonotonic additive risk measures from acceptance sets.
method Conditions on acceptance sets for induced comonotonic additive risk measures.
result Acceptance sets induce comonotonic additive risk measures if and only if the acceptance sets and their complements are stable under convex combinations of comonotonic random variables.
Paper introduces new approximations for lognormal sums, matching comonotonicity and moments.
problem Approximating sums of lognormal random variables accurately.
method Introduces new approximations based on weighted distribution theory, emphasizing comonotonicity and moment matching.
result Approximations perform better than classical methods, especially in the right tail of the distribution.
New property shows VaR subadditivity for comonotonic loss variables.
problem Understanding VaR subadditivity and comonotonicity.
method Analyzes VaR subadditivity and comonotonicity relationship.
result VaR subadditivity holds for comonotonic loss variables.
This paper reviews incompatibilities of comonotonic risk measures.
problem Incompatibilities of comonotonic risk measures with central properties.
method Literature review and Choquet representation of comonotonic additive risk measures.
result Comonotonic additive risk measures cannot be surplus invariant.
We give a complete characterization of both comonotone and not comonotone coherent risk measures in the discrete finite probability space, where each outcome is equally likely. To the best of our knowledge, this is the first work that characterizes \textit{and} distinguishes comonotone and not comonotone coherent risk …
Within the context of capital adequacy, we study comonotonicity of risk measures in terms of the primitives of the theory: acceptance sets and eligible, or reference, assets. We show that comonotonicity cannot be characterized by the properties of the acceptance set alone and heavily depends on the choice of the eligib…
In this paper we present formulas for the valuation of debt and equity of firms in a financial network under comonotonic endowments. We demonstrate that the comonotonic setting provides a lower bound and Jensen's inequality provides an upper bound to the price of debt under Eisenberg-Noe financial networks with bankrup…
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.
The paper explores non-convex risk measures and their characterizations.
problem Characterizing non-convex risk measures without convexity or weak convexity.
method Characterizes monetary risk measures as lower envelopes of families of convex or coherent risk measures, considering law-invariance and SSD-consistency.
result Unified representation theorems for law-invariant risk measures, including VaR.
It is well known that a random vector with given marginal distributions is comonotonic if and only if it has the largest sum with respect to the convex order [ Kaas, Dhaene, Vyncke, Goovaerts, Denuit (2002), A simple geometric proof that comonotonic risks have the convex-largest sum, ASTIN Bulletin 32, 71-80. Cheung (2…
In this paper we introduce a new multivariate dependence measure based on comonotonicity by means of product moment which motivated by the recent papers of Koch and Schepper (ASTIN Bulletin 41 (2011) 191-213) and Dhaene et al. (Journal of Computational and Applied Mathematics 263 (2014) 78-87). Some differences and rel…
Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticised for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES is less straightforward…
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.
It is well-known that an R-valued random vector (X1,X2,⋯,Xn) is comonotonic if and only if (X1,X2,⋯,Xn) and (Q1(U),Q2(U),⋯,Qn(U)) coincide \emph{in distribution}, for \emph{any} random variable U uniformly distributed on the unit interval (0,1), where Qk(⋅) ar…
The paper examines bounds for stop-loss payoffs using transformed random variables.
problem Bounding stop-loss payoffs for a difference of two random variables.
method Analyzes crossing points of cdfs of original and transformed random variables.
result Unique pairwise crossing points for mortality-linked securities under symmetric copulas.
Proposes counterfactual explainability for causal attribution, extending variance analysis methods.
problem Lack of mechanistic understanding in existing tools for explaining complex models.
method Extends global sensitivity analysis methods to causal explanations using directed acyclic graphs.
result Developed methods to estimate counterfactual explainability and applied to income inequality analysis.
New optimal transport divergences derived from scoring functions.
problem Developing new divergences for optimal transport.
method Using scoring functions as cost functions in optimal transport.
result Comonotonic coupling is optimal for many new divergences.
In [16], a new family of vector-valued risk measures called multivariate expectiles is introduced. In this paper, we focus on the asymptotic behavior of these measures in a multivariate regular variations context. For models with equivalent tails, we propose an estimator of these multivariate asymptotic expectiles, in …
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. …
Paper investigates Lambda Value-at-Risk under ambiguity and risk sharing.
problem Investigates Lambda Value-at-Risk under ambiguity and risk sharing.
method Establishes equivalence of robust ΛVaR and traditional ΛVaR under ambiguity sets, analyzes properties, derives explicit formulas, and explores risk sharing. result Unified and extended the concept of Value-at-Risk under ambiguity, derived explicit formulas for specific ambiguity sets, and explored risk sharing.
Optimizes dynamic investment portfolios with correlated jumps.
problem Maximizing expected terminal wealth in a multivariate Merton model with dependent jumps.
method Approximating CVaR with comonotonic bounds and maximizing expected terminal wealth.
result Improved optimization of dynamic investment portfolios.
Study efficient numerical methods for American basket options.
problem Valuation of American basket options.
method Partial differential complementarity problems (PDCPs) and efficient discretization.
result Approximations of American basket options are close and converge favourably.
Calibrating classifiers reduces grouping loss using sufficiency criteria.
problem Grouping loss in probabilistic classifier calibration is often overlooked.
method Revisited Langford & Zadrozny's probing reduction approach and introduced Brier curves.
result The probing reduction approach reduces grouping loss and supports sufficient calibration.
Risk measures such as Expected Shortfall (ES) and Value-at-Risk (VaR) have been prominent in banking regulation and financial risk management. Motivated by practical considerations in the assessment and management of risks, including tractability, scenario relevance and robustness, we consider theoretical properties of…
We introduce a non-parametric method to recover physical probability distributions of asset returns based on their European option prices and some other sparse parametric information. Thus the main problem is similar to the one considered foir instance in the Recovery Theorem by Ross (2015), except that here we conside…
The paper optimizes DIA purchase policies using lifecycle models and asset allocation.
problem Determining the optimal allocation to Deferred Income Annuities (DIAs).
method Employed a lifecycle model with utility of consumption and bequest, formalized optimization process, analyzed results, and extended model to include asset allocation.
result Optimal DIA allocation varies based on refundability, asset allocation, and perceived longevity.
Study optimizes resource allocation in noisy systems for better control.
problem Limited attention in stochastic systems with multiplicative noise.
method Analytical and numerical methods for optimal attention allocation.
result Effective resource allocation enhances noise estimation and control decisions.
The paper proposes an asset allocation strategy using the Sortino ratio for better performance.
problem Traditional asset allocation methods like the Sharpe ratio do not penalize negative returns adequately.
method The Sortino ratio is used to maximize asset allocation, penalizing only negative return variances.
result The Sortino ratio-based strategy outperforms traditional methods like the Kelly criterion.
This paper tackles post-trade allocation inefficiencies and presents a uniform return allocation method.
problem Return divergence among accounts after trade allocation.
method Systematic treatment of trade allocation risk, presenting a uniform return allocation method.
result Uniform allocation of returns irrespective of the number of accounts and trade sizes.
This paper examines allocation mechanisms in markets with transfer costs, showing how these costs affect economic efficiency.
problem Transfer costs in decentralized exchange markets reduce economic efficiency.
method An axiomatic study of allocation mechanisms in the presence of transfer costs, providing robust and conditional mean allocation mechanisms.
result Robust and conditional mean allocation mechanisms are identified, relating to risk sharing in agent pools.
Paper introduces a new method for allocating capital based on risk measures from ruin theory.
problem Allocating capital to manage risk measures derived from ruin theory.
method Introduces a novel allocation method for dynamic value-at-risk (VaR) measures.
result Demonstrates desirable properties and compares with existing methods.
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…
Framework uses hindsight regret to audit marketing budget allocations.
problem Lack of principled way to assess strategic budget allocations.
method Hindsight regret framework based on constraint-faithful benchmark.
result Identifies practical trade-off between allocation flexibility and detectability.
New method allocates capital based on tail central moments for financial risk assessment.
problem Inability of CTE-based capital allocation to reflect tail behavior of losses.
method Developed TCM-based capital allocation for normal mean-variance mixture distributions.
result TCM-based method captures tail risk contributions not detected by CTE.
The paper explores capital allocation using Euler formula with VaR and ES, revealing non-monotonicity and providing estimation methods.
problem Non-monotonicity in VaR-based capital allocation and the need for consistent risk measures.
method Use of Euler formula, Value-at-Risk (VaR), Expected shortfall (ES), simulation, and Markov chain Monte Carlo.
result Capital allocation with VaR is not monotonous, and consistent risk measures are crucial.
Capital allocation principles are used in various contexts in which a risk capital or a cost of an aggregate position has to be allocated among its constituent parts. We study capital allocation principles in a performance measurement framework. We introduce the notation of suitability of allocations for performance me…
The financial crisis showed the importance of measuring, allocating and regulating systemic risk. Recently, the systemic risk measures that can be decomposed into an aggregation function and a scalar measure of risk, received a lot of attention. In this framework, capital allocations are added after aggregation and can…
The paper analyzes insurance pricing and capital allocation in imperfect markets.
problem Analyzing insurance pricing and capital allocation in imperfect markets.
method Non-additive distortion pricing functional and principle of equal priority of payments in default.
result Derives the natural allocation of premium and margin with properties that merit the name.
The expectile can be considered as a generalization of quantile. While expected shortfall is a quantile based risk measure, we study its counterpart -- the expectile based expected shortfall -- where expectile takes the place of quantile. We provide its dual representation in terms of Bochner integral. Among other prop…