arXiv research

This paper examines if CTE risk measure aligns with profit-maximizing risk capital allocations.

The paper calculates VaR and CTE for extreme and aggregate risks using FGM copula.

New method allocates capital based on tail central moments for financial risk assessment.

A usual reinsurance policy for insurance companies admits one or two layers of the payment deductions. Under optimal criterion of minimizing the conditional tail expectation (CTE) risk measure of the insurer's total risk, this article generalized an optimal stop-loss reinsurance policy to an optimal multi-layer reinsur…

CTE improves explanation estimation with less data and faster computation.

Predicts long-term return distributions with time-varying volatility.

The paper proposes a new framework to generate synthetic data with human-like imperfections to prevent model collapse.

A new method synthesizes expressions from characteristics using GAN for healthcare.

We show uniqueness for overdetermined elliptic problems defined on topological disks $Ω$ with $C^2$ boundary, i.e., positive solutions $u$ to $Δu + f(u)=0$ in $Ω\subset (M^2,g)$ so that $u = 0$ and $\frac{\partial u}{\partial \vecη} = cte$ along $\partial Ω$, $\vecη$ the unit outward normal along $\partialΩ$ under the…

New set-valued star-shaped risk measures introduced for better risk assessment.

Paper characterizes star-shaped risk measures and their properties.

Introduces factor risk measures to assess risk relative to multiple factors.

The paper studies dynamic star-shaped risk measures and their representation.

The paper establishes a connection between different risk measures and their risk contributions.

Paper introduces quasi-logconvex risk measures and their properties.

Submodularity is studied for convex risk measures, including Expected Shortfall.

Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their risk-aversion functions. To date there has been very little guidance on the choice of risk-aversion functions underlying spectral risk measures. This paper addresses this issue by examining two popular …

The paper explores non-convex risk measures and their characterizations.

Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set minimization problems. The dual relationship between these two classes of multivariate ris…

Study risk-sensitive reinforcement learning with Lipschitz dynamic risk measures, establishing regret bounds.

Develops a new method for risk diversification using dynamic risk measures.

Paper introduces new risk measures that unify two existing types.

New risk measures for financial and ESG risks using utility functions.

Dual representations for robust risk measures and uncertainty sets.

New risk measures assess cryptocurrency market vulnerabilities during financial distress.

A new measure quantifies how risk-averse different risk measures are.

Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize loss-based risk measures by a representation theorem and give examples of su…

Study asymptotic properties of generalized shortfall risk measures for heavy-tailed risks.

Study distortion risk measures for step-weighted distributions.

New risk measure considers horizon risk and interest rate uncertainty.

New risk measures adjust for tail risk inadequacies.

This paper was presented and written for two seminars: a national UK University Risk Conference and a Risk Management industry workshop. The target audience is therefore a cross section of Academics and industry professionals. The current ongoing global credit crunch has highlighted the importance of risk measurement i…

Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their subjective risk-aversion. This paper examines spectral risk measures based on an exponential utility function, and finds that these risk measures have nice intuitive properties. It also discusses how th…

This paper shows how to calculate risk measures for sums of two counter-monotonic risks.

Investigates set-valued risk measures for processes and vectors, proving equivalence and providing new dual representations.

This paper introduces a new systemic risk measure, JMES, and its associated contribution measures.

New method tests risk measures for various distortions.

Develops a statistical framework for coherent risk estimation.

Study risk sharing among agents with varying risk preferences.

We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional aggregation and a univariate conditional risk measure. Our studies extend known results f…

Paper studies convex risk measures linked to optimization.

A new class of risk measures called cash sub-additive risk measures is introduced to assess the risk of future financial, nonfinancial and insurance positions. The debated cash additive axiom is relaxed into the cash sub additive axiom to preserve the original difference between the numeraire of the current reserve amo…

We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural definition of vector-valued risk measures. Several main constructions of risk meas…

Paper characterizes monotonic mean-deviation risk measures.

We characterize when a convex risk measure associated to a law-invariant acceptance set in $L^\infty$ can be extended to $L^p$, $1\leq p<\infty$, preserving finiteness and continuity. This problem is strongly connected to the statistical robustness of the corresponding risk measures. Special attention is paid to concre…

This paper presents non-parametric estimates of spectral risk measures applied to long and short positions in 5 prominent equity futures contracts. It also compares these to estimates of two popular alternative measures, the Value-at-Risk (VaR) and Expected Shortfall (ES). The spectral risk measures are conditioned on …

We present a general framework for measuring the liquidity risk. The theoretical framework defines a class of risk measures that incorporate the liquidity risk into the standard risk measures. We consider a one-period risk measurement model. The liquidity risk is defined as the risk that a given security or a portfolio…

Extends return risk measures to multiple assets, proving properties and comparing different risk models.