arXiv subjects

Christian Laudagé

Publications and source records attributed to Christian Laudagé.

7 recordsLinked to original sources

arXiv2026

Meyer risk measures

Risk measures summarize the risk profile of financial positions in a single metric, which allows their comparison and supports investment decisions. When they respect common stochastic orders such as second-order stochastic dominance (SSD), they rest on sound conceptual grounds. Since SSD can be overly conservative and rigid, we study Meyer risk measures. Those are monetary risk measures that are consistent with stochastic orders induced by a threshold utility function $v$, where the defining test utilities are at least as risk averse as $v$. The flexibility in choosing $v$ allows to encompass a wide range of stochastic orders, including SSD. Our contribution is threefold. First, we show that Meyer risk measures whose threshold utility $v$ is CARA admit a lower envelope representation via adjusted risk measures, and analyse how they extend and compare to classical risk measures. Second, we show that monotone additive statistics, recently introduced in decision theory, are Meyer risk measures under mild conditions. Third, impossibility results for the situation beyond the CARA class establish that monetary risk measures compatible to the associated stochastic orders either fail to exist or cannot satisfy key properties simultaneously. Throughout, we highlight practical implications, for example to portfolio selection and risk management.

q-fin.MF↗

arXiv2026

Geometrically convex return risk measures on AM-algebras

Monetary risk measures quantify the risk of uncertain monetary payoffs (or losses), whereas in time series analysis risk is typically assessed using logarithmic returns. Return risk measures (RRMs) provide an axiomatic foundation for the latter approach, which relies crucially on the positive cone of the space of essentially bounded random variables. We extend RRMs to general ordered vector spaces and characterize positive homogeneity via the geometric epigraph. To investigate geometric convexity and establish connections with monetary risk measures, we specialize the domain as a subset of an AM-algebra, encompassing Euclidean spaces and spaces of multidimensional essentially bounded random variables. The latter is novel in the context of RRMs and leads to the new classes of systemic and vector-valued RRMs. We establish results on finiteness, continuity, separability, as well as dual and aggregation-based representations.

q-fin.MF↗

arXiv2026

PELVE from a regulatory perspective

Under Solvency II, the Value-at-Risk (VaR) is applied, although there is broad consensus that the Expected Shortfall (ES) constitutes a more appropriate risk measure. Moving towards ES would necessitate specifying the corresponding ES level. The recently introduced Probability Equivalent Level of VaR and ES (PELVE) determines this by requiring that ES equals the prescribed VaR for a given future payoff, reflecting the situation of an individual insurer. We incorporate the regulator's perspective by proposing PELVE-inspired methods for multiple insurers. We analyze existence and uniqueness of the resulting ES levels, derive expressions for elliptically distributed payoffs and establish limit results for multivariate regularly distributed payoffs. A case study highlights that the choice of method is crucial when payoffs arise from different distribution families. We provide recommendations which of our PELVE-inspired methods are most appropriate in certain scenarios.

q-fin.MF↗

arXiv2025

Risk measures based on target risk profiles

We address the problem that classical risk measures may not detect the tail risk adequately. This can occur for instance due to averaging when calculating the Expected Shortfall. The current literature proposes the so-called adjusted Expected Shortfall as a solution. This risk measure is the supremum of Expected Shortfalls for all possible levels, adjusted with a function $g$, the so-called target risk profile. We generalize this idea by using a family of risk measures which allows for more choices than Expected Shortfalls, leading to the concept of adjusted risk measures. An adjusted risk measure quantifies the minimal amount of capital that has to added to a financial position $X$ to ensure that each risk measure out of the chosen family is smaller or equal to the target risk profile $g(p)$ for the corresponding level $p\in[0,1]$. We discuss a variety of assumptions such that desirable properties for risk measures are satisfied in this setup. From a theoretical point of view, our main contribution is the analysis of equivalent assumptions such that an adjusted risk measure is positive homogeneous and subadditive. Furthermore, we show that these conditions hold for several adjusted risk measures beyond the adjusted Expected Shortfall. In addition, we derive their dual representations. Finally, we test the performance in a case study based on the S$\&$P $500$.

q-fin.MF↗

arXiv2025

Multi-asset return risk measures

We revisit the recently introduced concept of return risk measures (RRMs) and extend it by incorporating risk management via multiple so-called eligible assets. The resulting new class of risk measures, termed multi-asset return risk measures (MARRMs), introduces a novel economic model for multiplicative risk sharing. We analyze properties of these risk measures. In particular, we prove that a positively homogeneous MARRM is quasi-convex if and only if it is convex. Furthermore, we provide conditions to avoid inconsistent risk evaluations. Then, we point out the connection between MARRMs and the well-known concept of multi-asset risk measures (MARMs). This is used to obtain various dual representations of MARRMs. Moreover, we conduct a series of case studies, in which we use typical continuous-time financial markets and different notions of acceptability of losses to compare RRMs, MARMs, and MARRMs and draw conclusions about the cost of risk mitigation.

q-fin.MF↗

arXiv2025

Quantum Risk Analysis: Beyond (Conditional) Value-at-Risk

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 introduced to calculate them. These procedures are based on the so-called quantum amplitude estimation algorithm which lead to a quadratic speed up compared to classical Monte-Carlo based methods. Based on these ideas, we construct quantum-based algorithms to calculate alternatives for VaR and CVaR, namely the Expectile Value-at-Risk (EVaR) and the Range Value-at-Risk (RVaR). We construct quantum algorithms to calculate them. These algorithms are based on quantum amplitude estimation. In a case study, we compare their performance with the quantum-based algorithms for VaR and CVaR. We find that all of the algorithms perform sufficiently well on a quantum simulator. Further, the calculations of EVaR and VaR are robust against noise on a real quantum device. This is not the case for CVaR and RVaR.

quant-ph↗

arXiv2024

A Comparative Study of Factor Models for Different Periods of the Electricity Spot Price Market

Due to major shifts in European energy supply, a structural change can be observed in Austrian electricity spot price data starting from the second quarter of the year 2021 onward. In this work we study the performance of two different factor models for the electricity spot price in three different time periods. To this end, we consider three samples of EEX data for the Austrian base load electricity spot price, one from the pre-crises from 2018 to 2021, the second from the time of the crisis from 2021 to 2023 and the whole data from 2018 to 2023. For each of these samples, we investigate the fit of a classical 3-factor model with a Gaussian base signal and one positive and one negative jump signal and compare it with a 4-factor model to assess the effect of adding a second Gaussian base signal to the model. For the calibration of the models we develop a tailor-made Markov Chain Monte Carlo method based on Gibbs sampling. To evaluate the model adequacy, we provide simulations of the spot price as well as a posterior predictive check for the 3- and the 4-factor model. We find that the 4-factor model outperforms the 3-factor model in times of non-crises. In times of crises, the second Gaussian base signal does not lead to a better fit of the model. To the best of our knowledge, this is the first study regarding stochastic electricity spot price models in this new market environment. Hence, it serves as a solid base for future research.

q-fin.MF↗