arXiv subjects

Ilaria Peri

Publications and source records attributed to Ilaria Peri.

10 recordsLinked to original sources

arXiv2026

Numerical methods for lambda quantiles: robust evaluation and portfolio optimisation

Lambda quantiles, originally introduced as lambda value at risk, generalise the classical value at risk by allowing for a variable confidence level. This work presents efficient algorithms for computing lambda quantiles and demonstrates their application in portfolio optimisation. We first develop a robust algorithm, {\Lambda}-Newton-Bis, that combines Newton's method with a bisection strategy to ensure global convergence. The algorithm handles potential discontinuities and achieves local quadratic convergence under standard regularity assumptions. To address cases with multiple roots, we also propose an interval analysis approach. We then demonstrate the algorithm's computational efficiency and practical relevance within a portfolio optimization framework. To this end, we develop two alternative solution methods that incorporate the {\Lambda}-Newton-Bis procedure. Numerical experiments confirm the algorithm's convergence properties and highlight its computational advantages in optimization tasks based on lambda quantiles.

q-fin.CP↗

arXiv2026

Ranking Metrics: Extending Acceptability and Performance Indexes

This paper develops an axiomatic framework for ranking metrics, a general class of functionals for evaluating and ordering financial or insurance positions. Unlike traditional risk-adjusted performance measures-such as the Sharpe ratio, RAROC, or Omega-that express reward per unit of risk, ranking metrics assign each position a performance level rather than a normalized return. Relying on monotonicity and a new property called cash-quasiconcavity, we derive representation results linking ranking metrics to families of acceptance sets and risk measures, extending the theory of acceptability indices. Classical ratios arise as special cases, while new examples-based on expected-loss, Lambda-quantile, and bibliometric indices-illustrate the framework's flexibility. Empirical applications to portfolio ranking and climate-risk insurance demonstrate its practical relevance.

q-fin.RM↗

arXiv2025

Constructing elicitable risk measures

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 possesses properties such as monotonicity, translation invariance, convexity, and positive homogeneity. Our framework encompasses the majority of well-known elicitable risk measures including all elicitable convex and coherent risk measures. Our setting moreover allows to construct novel elicitable risk measures that are, for example, convex but not coherent. Furthermore, we discuss how higher-order elicitability, such as jointly eliciting the mean and variance or different quantile levels, fall within our setting.

q-fin.MF↗

arXiv2022

Risk contributions of lambda quantiles

Risk contributions of portfolios form an indispensable part of risk adjusted performance measurement. The risk contribution of a portfolio, e.g., in the Euler or Aumann-Shapley framework, is given by the partial derivatives of a risk measure applied to the portfolio profit and loss in direction of the asset units. For risk measures that are not positively homogeneous of degree 1, however, known capital allocation principles do not apply. We study the class of lambda quantile risk measures that includes the well-known Value-at-Risk as a special case but for which no known allocation rule is applicable. We prove differentiability and derive explicit formulae of the derivatives of lambda quantiles with respect to their portfolio composition, that is their risk contribution. For this purpose, we define lambda quantiles on the space of portfolio compositions and consider generic (also non-linear) portfolio operators. We further derive the Euler decomposition of lambda quantiles for generic portfolios and show that lambda quantiles are homogeneous in the space of portfolio compositions, with a homogeneity degree that depends on the portfolio composition and the lambda function. This result is in stark contrast to the positive homogeneity properties of risk measures defined on the space of random variables which admit a constant homogeneity degree. We introduce a generalised version of Euler contributions and Euler allocation rule, which are compatible with risk measures of any homogeneity degree and non-linear but homogeneous portfolios. These concepts are illustrated by a non-linear portfolio using financial market data.

q-fin.RM↗

arXiv2022

A Hybrid Model for Forecasting Short-Term Electricity Demand

Currently the UK Electric market is guided by load (demand) forecasts published every thirty minutes by the regulator. A key factor in predicting demand is weather conditions, with forecasts published every hour. We present HYENA: a hybrid predictive model that combines feature engineering (selection of the candidate predictor features), mobile-window predictors and finally LSTM encoder-decoders to achieve higher accuracy with respect to mainstream models from the literature. HYENA decreased MAPE loss by 16\% and RMSE loss by 10\% over the best available benchmark model, thus establishing a new state of the art for the UK electric load (and price) forecasting.

cs.LG↗

arXiv2022

An axiomatization of $Λ$-quantiles

We give an axiomatic foundation to $Λ$-quantiles, a family of generalized quantiles introduced by Frittelli et al. (2014) under the name of Lambda Value at Risk. Under mild assumptions, we show that these functionals are characterized by a property that we call "locality", that means that any change in the distribution of the probability mass that arises entirely above or below the value of the $Λ$-quantile does not modify its value. We compare with a related axiomatization of the usual quantiles given by Chambers (2009), based on the stronger property of "ordinal covariance", that means that quantiles are covariant with respect to increasing transformations. Further, we present a systematic treatment of the properties of $Λ$-quantiles, refining some of the results of Frittelli et al. (2014) and Burzoni et al. (2017) and showing that in the case of a nonincreasing $Λ$ the properties of $Λ$-quantiles closely resemble those of the usual quantiles.

q-fin.MF↗

arXiv2017

Backtesting Lambda Value at Risk

A new risk measure, the lambda value at risk (Lambda VaR), has been recently proposed from a theoretical point of view as a generalization of the value at risk (VaR). The Lambda VaR appears attractive for its potential ability to solve several problems of the VaR. In this paper we propose three nonparametric backtesting methodologies for the Lambda VaR which exploit different features. Two of these tests directly assess the correctness of the level of coverage predicted by the model. One of these tests is bilateral and provides an asymptotic result. A third test assess the accuracy of the Lambda VaR that depends on the choice of the P&L distribution. However, this test requires the storage of more information. Finally, we perform a backtesting exercise and we compare our results with the ones from Hitaj and Peri (2015)

q-fin.RM↗

arXiv2017

On the properties of the Lambda value at risk: robustness, elicitability and consistency

Recently, financial industry and regulators have enhanced the debate on the good properties of a risk measure. A fundamental issue is the evaluation of the quality of a risk estimation. On the one hand, a backtesting procedure is desirable for assessing the accuracy of such an estimation and this can be naturally achieved by elicitable risk measures. For the same objective, an alternative approach has been introduced by Davis (2016) through the so-called consistency property. On the other hand, a risk estimation should be less sensitive with respect to small changes in the available data set and exhibit qualitative robustness. A new risk measure, the Lambda value at risk (Lambda VaR), has been recently proposed by Frittelli et al. (2014), as a generalization of VaR with the ability to discriminate the risk among P&L distributions with different tail behaviour. In this article, we show that Lambda VaR also satisfies the properties of robustness, elicitability and consistency under some conditions.

q-fin.RM↗

arXiv2012

Risk Measures on $\mathcal{P}(\mathbb{R})$ and Value At Risk with Probability/Loss function

We propose a generalization of the classical notion of the $V@R_λ$ that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by defining a new class of law invariant risk measures based on an appropriate family of acceptance sets. The $V@R_λ$ and other known law invariant risk measures turn out to be special cases of our proposal. We further prove the dual representation of Risk Measures on $\mathcal{P}(% \mathbb{R}).$

q-fin.RM↗

arXiv2012

From Risk Measures to Research Measures

In order to evaluate the quality of the scientific research, we introduce a new family of scientific performance measures, called Scientific Research Measures (SRM). Our proposal originates from the more recent developments in the theory of risk measures and is an attempt to resolve the many problems of the existing bibliometric indices. The SRM that we introduce are based on the whole scientist's citation record and are: coherent, as they share the same structural properties; flexible to fit peculiarities of different areas and seniorities; granular, as they allow a more precise comparison between scientists, and inclusive, as they comprehend several popular indices. Another key feature of our SRM is that they are planned to be calibrated to the particular scientific community. We also propose a dual formulation of this problem and explain its relevance in this context.

q-fin.RM↗