arXiv subjects

Silvana M. Pesenti

Publications and source records attributed to Silvana M. Pesenti.

At least 19 recordsLinked to original sources

arXiv2026

Dynamic Portfolio Optimization under CVaR Constraints

We study continuous-time dynamic portfolio optimization under a Conditional Value-at-Risk (CVaR) constraint on the investor's terminal loss. For a general class of convex trading objectives, we exploit the auxiliary-threshold representation of CVaR to establish the existence of an optimal strategy and strong duality without requiring market completeness. These results motivate a dual-based nested bisection--golden-search algorithm over the threshold and Lagrangian multiplier, where the inner iterations reduce to standard unconstrained stochastic control problems. We prove that the resulting strategies converge to the optimal control as the number of iterations tends to infinity. Numerical experiments recover the Merton policy when the risk constraint is nonbinding. When the constraint is binding, the optimal strategy becomes state dependent: the investor reduces risky exposure following adverse outcomes but preserves, and near maturity may increase, exposure following favorable outcomes. Thus, a terminal CVaR constraint produces an asymmetric reallocation across states rather than uniform de-risking. Nontraded endowment risk amplifies the conservative adjustment, whereas price impact lowers desired positions and adjustment speeds.

math.OC↗

arXiv2026

Bounds for Distributionally Robust Optimization Problems

We study distributionally robust optimization (DRO) problems with uncertainty sets consisting of high-dimensional random vectors that are close in the multivariate Wasserstein distance to a reference random vector. We give conditions when the images of these sets under scalar-valued aggregation functions are contained in and contain uncertainty sets of univariate random variables defined via a univariate Wasserstein distance. This provides lower and upper bounds for the solution to general multivariate DRO problems that are computationally tractable. Furthermore, we generalize the results to uncertainty sets characterized by Bregman-Wasserstein divergences, which allows for asymmetric deviations from the reference random vector. Moreover, for DRO problems with risk measure criterion in the class of signed Choquet integrals, we derive semi-analytic formulae for the upper and lower bounds and the distribution that attains these bounds.

math.OC↗

arXiv2026

Adapted Law Invariance and Time-Consistent Dynamic Risk Measures

In static risk measurement, law invariance expresses the principle that the risk of a position should depend only on its distribution, and not on the particular probability space on which it is represented. In a dynamic setting, the same principle leads naturally to adapted law invariance: the risk assessment should depend only on the probabilistic structure of the financial position together with the way information about it is revealed over time. We show that, for time-consistent risk measures, adapted law invariance is equivalent to a recursive one-step conditional-law representation. More precisely, assuming Fatou regularity, the one-step risk evaluations are exactly conditional lifts of static law-invariant risk measures, and the full dynamic risk measure is obtained by backward composition of these one-step maps. Convexity and coherence of the dynamic risk measure are characterized by the corresponding properties of the static one-step risk measures. This identifies adapted law invariance as the dynamic counterpart of ordinary law invariance. It also clarifies the strength of terminal-law invariance, as it appears in the rigidity theorem of Kupper and Schachermayer: it does not distinguish risks with the same distribution but different times of resolution. We further obtain an adapted Kusuoka representation in the coherent case and establish an extension of the Kupper--Schachermayer theorem.

q-fin.RM↗

arXiv2026

Preference robust distortion risk measures

We introduce a framework for preference-robust decision making when preferences over risk are modelled through generalised distortion risk measures. Unlike distributional robustness, our approach addresses ambiguity in the risk functional itself. We construct ambiguity sets on distortion (weight) functions using the Wasserstein distance and Bregman divergences, and derive closed-form expressions for the worst- and best-case distortion risk measures. We further extend the framework to rank-dependent utility, yielding preference-robust behavioural models. In particular, rank-dependent utility appears as a robustification of the expected utility model, yielding a novel way to address the Allais paradox.

q-fin.RM↗

arXiv2026

Model Combination in Risk Sharing under Ambiguity

We consider the problem of an agent who faces losses in continuous time over a finite time horizon and may choose to share some of these losses with a counterparty. The agent is uncertain about the true loss distribution and has multiple models for the losses, characterized by a finite set of probability measures. Their goal is to optimize a mean-variance type criterion with model combination under ambiguity through risk sharing. We construct such a criterion using the chi-squared divergence, exploiting a dual representation to expand the state space, yielding a time consistent problem. Assuming a Cramér-Lundberg loss model, we fully characterize the optimal risk sharing contract and the agent's wealth process under the optimal strategy. We prove that the strategy we obtain is admissible and that the value function satisfies the appropriate verification conditions. Furthermore, we show that the model combination problem is equivalent to the monotone mean-variance problem of Maccheroni et al. (2009) under a composite probability measure that depends on the agent's reference probability measures. Finally, we apply the optimal strategy to an insurance setting in a simulation example and provide numerical illustrations of the results.

q-fin.RM↗

arXiv2026

Dual Representation of Robust Risk Measures and Uncertainty Sets

We consider robust risk measures that arise as worst-case values of convex risk measures evaluated on uncertainty sets. We characterize continuity properties of robust risk measures through their consolidated uncertainty sets, derive dual representations for robust risk measures, and develop a set-valued dual representation for consolidated uncertainty sets. The two dual frameworks rely on distinct geometric assumptions and are therefore complementary rather than interchangeable.

q-fin.RM↗

arXiv2026

Optimal payoff under Bregman-Wasserstein divergence constraints

We study optimal payoff choice for an expected utility maximizer under the constraint that their payoff is not allowed to deviate ``too much'' from a given benchmark. We solve this problem when the deviation is assessed via a Bregman-Wasserstein (BW) divergence, generated by a convex function $ϕ$. Unlike the Wasserstein distance (i.e., when $ϕ(x)=x^2$) the inherent asymmetry of the BW divergence makes it possible to penalize positive deviations different than negative ones. As a main contribution, we provide the optimal payoff in this setting. Numerical examples illustrate that the choice of $ϕ$ allow to better align the payoff choice with the objectives of investors.

q-fin.PM↗

arXiv2026

Outperforming a Benchmark with $α$-Bregman Wasserstein divergence

We consider the problem of active portfolio management, where an investor seeks the portfolio with maximal expected utility of the difference between the terminal wealth of their strategy and a proportion of the benchmark's, subject to a budget and a deviation constraint from the benchmark portfolio. As the investor aims at outperforming the benchmark, they choose a divergence that asymmetrically penalises gains and losses as well as penalises underperforming the benchmark more than outperforming it. This is achieved by the recently introduced $α$-Bregman-Wasserstein divergence, subsuming the Bregman-Wasserstein and the popular Wasserstein divergence. We prove existence and uniqueness, characterise the optimal portfolio strategy, and give explicit conditions when the divergence constraints and the budget constraints are binding. We conclude with a numerical illustration of the optimal quantile function in a geometric Brownian motion market model.

q-fin.PM↗

arXiv2026

Dynamic Pareto Optima in Multi-Period Pure-Exchange Economies

We study a problem of optimal allocation in a discrete-time multi-period pure-exchange economy, where agents have preferences over stochastic endowment processes that are represented by strongly time-consistent dynamic risk measures. We introduce the notion of dynamic Pareto-optimal allocation processes and show that such processes can be constructed recursively starting with the allocation at the terminal time. We further derive a comonotone improvement theorem for allocation processes, and we provide a recursive approach to constructing comonotone dynamic Pareto optima when the agents' preferences are coherent and satisfy a property that we call equidistribution-preserving. In the special case where each agent's dynamic risk measure is of the distortion type, we provide a closed-form characterization of comonotone dynamic Pareto optima. We illustrate our results in a two-period setting.

q-fin.RM↗

arXiv2025

Distributional regression for seasonal data: an application to river flows

Risk assessment in casualty insurance, such as flood risk, traditionally relies on extreme-value methods that emphasizes rare events. These approaches are well-suited for characterizing tail risk, but do not capture the broader dynamics of environmental variables such as moderate or frequent loss events. To complement these methods, we propose a modelling framework for estimating the full (daily) distribution of environmental variables as a function of time, that is a distributional version of typical climatological summary statistics, thereby incorporating both seasonal variation and gradual long-term changes. Aside from the time trend, to capture seasonal variation our approach simultaneously estimates the distribution for each instant of the seasonal cycle, without explicitly modelling the temporal dependence present in the data. To do so, we adopt a framework inspired by GAMLSS (Generalized Additive Models for Location, Scale, and Shape), where the parameters of the distribution vary over the seasonal cycle as a function of explanatory variables depending only on the time of year, and not on the past values of the process under study. Ignoring the temporal dependence in the seasonal variation greatly simplifies the modelling but poses inference challenges that we clarify and overcome. We apply our framework to daily river flow data from three hydrometric stations along the Fraser River in British Columbia, Canada, and analyse the flood of the Fraser River in early winter of 2021.

stat.AP↗

arXiv2025

Marginal Fairness: Fair Decision-Making under Risk Measures

This paper introduces marginal fairness, a new individual fairness notion for equitable decision-making in the presence of protected attributes such as gender, race, and religion. This criterion ensures that decisions based on generalized distortion risk measures are insensitive to distributional perturbations in protected attributes, regardless of whether these attributes are continuous, discrete, categorical, univariate, or multivariate. To operationalize this notion and reflect real-world regulatory environments (such as the EU gender-neutral pricing regulation), we model business decision-making in highly regulated industries (such as insurance and finance) as a two-step process: (i) a predictive modeling stage, in which a prediction function for the target variable (e.g., insurance losses) is estimated based on both protected and non-protected covariates; and (ii) a decision-making stage, in which a generalized distortion risk measure is applied to the target variable, conditional only on non-protected covariates, to determine the decision. In this second step, we modify the risk measure such that the decision becomes insensitive to the protected attribute, thus enforcing fairness to ensure equitable outcomes under risk-sensitive, regulatory constraints. Furthermore, by utilizing the concept of cascade sensitivity, we extend the marginal fairness framework to capture how dependencies between covariates propagate the influence of protected attributes through the modeling pipeline. A numerical study and an empirical implementation using an auto insurance dataset demonstrate how the framework can be applied in practice.

stat.ML↗

arXiv2025

Kullback-Leibler Barycentre of Stochastic Processes

We consider the problem where an agent aims to combine the views and insights of different experts' models. Specifically, each expert proposes a diffusion process over a finite time horizon. The agent then combines the experts' models by minimising the weighted Kullback--Leibler divergence to each of the experts' models. We show existence and uniqueness of the barycentre model and prove an explicit representation of the Radon--Nikodym derivative relative to the average drift model. We further allow the agent to include their own constraints, resulting in an optimal model that can be seen as a distortion of the experts' barycentre model to incorporate the agent's constraints. We propose two deep learning algorithms to approximate the optimal drift of the combined model, allowing for efficient simulations. The first algorithm aims at learning the optimal drift by matching the change of measure, whereas the second algorithm leverages the notion of elicitability to directly estimate the value function. The paper concludes with an extended application to combine implied volatility smile models that were estimated on different datasets.

q-fin.MF↗

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↗

arXiv2025

Robust Elicitable Functionals

Elicitable functionals and (strictly) consistent scoring functions are of interest due to their utility of determining (uniquely) optimal forecasts, and thus the ability to effectively backtest predictions. However, in practice, assuming that a distribution is correctly specified is too strong a belief to reliably hold. To remediate this, we incorporate a notion of statistical robustness into the framework of elicitable functionals, meaning that our robust functional accounts for "small" misspecifications of a baseline distribution. Specifically, we propose a robustified version of elicitable functionals by using the Kullback-Leibler divergence to quantify potential misspecifications from a baseline distribution. We show that the robust elicitable functionals admit unique solutions lying at the boundary of the uncertainty region, and provide conditions for existence and uniqueness. Since every elicitable functional possesses infinitely many scoring functions, we propose the class of b-homogeneous strictly consistent scoring functions, for which the robust functionals maintain desirable statistical properties. We show the applicability of the robust elicitable functional in several examples: in a reinsurance setting and in robust regression problems.

stat.ME↗

arXiv2024

Risk Budgeting Allocation for Dynamic Risk Measures

We define and develop an approach for risk budgeting allocation - a risk diversification portfolio strategy - where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions that generalise the classical Euler contributions and which allow us to obtain dynamic risk contributions in a recursive manner. We prove that, for the class of coherent dynamic distortion risk measures, the risk allocation problem may be recast as a sequence of strictly convex optimisation problems. Moreover, we show that self-financing dynamic risk budgeting strategies with initial wealth of 1 are scaled versions of the solution of the sequence of convex optimisation problems. Furthermore, we develop an actor-critic approach, leveraging the elicitability of dynamic risk measures, to solve for risk budgeting strategies using deep learning.

q-fin.MF↗

arXiv2024

Optimal Robust Reinsurance with Multiple Insurers

We study a reinsurer who faces multiple sources of model uncertainty. The reinsurer offers contracts to $n$ insurers whose claims follow compound Poisson processes representing both idiosyncratic and systemic sources of loss. As the reinsurer is uncertain about the insurers' claim severity distributions and frequencies, they design reinsurance contracts that maximise their expected wealth subject to an entropy penalty. Insurers meanwhile seek to maximise their expected utility without ambiguity. We solve this continuous-time Stackelberg game for general reinsurance contracts and find that the reinsurer prices under a distortion of the barycentre of the insurers' models. We apply our results to proportional reinsurance and excess-of-loss reinsurance contracts, and illustrate the solutions numerically. Furthermore, we solve the related problem where the reinsurer maximises, still under ambiguity, their expected utility and compare the solutions.

q-fin.RM↗

arXiv2024

Differential Quantile-Based Sensitivity in Discontinuous Models

Differential sensitivity measures provide valuable tools for interpreting complex computational models used in applications ranging from simulation to algorithmic prediction. Taking the derivative of the model output in direction of a model parameter can reveal input-output relations and the relative importance of model parameters and input variables. Nonetheless, it is unclear how such derivatives should be taken when the model function has discontinuities and/or input variables are discrete. We present a general framework for addressing such problems, considering derivatives of quantile-based output risk measures, with respect to distortions to random input variables (risk factors), which impact the model output through step-functions. We prove that, subject to weak technical conditions, the derivatives are well-defined and derive the corresponding formulas. We apply our results to the sensitivity analysis of compound risk models and to a numerical study of reinsurance credit risk in a multi-line insurance portfolio.

stat.CO↗

arXiv2024

Optimal Transport Divergences induced by Scoring Functions

We employ scoring functions, used in statistics for eliciting risk functionals, as cost functions in the Monge-Kantorovich (MK) optimal transport problem. This gives raise to a rich variety of novel asymmetric MK divergences, which subsume the family of Bregman-Wasserstein divergences. We show that for distributions on the real line, the comonotonic coupling is optimal for the majority of the new divergences. Specifically, we derive the optimal coupling of the MK divergences induced by functionals including the mean, generalised quantiles, expectiles, and shortfall measures. Furthermore, we show that while any elicitable law-invariant coherent risk measure gives raise to infinitely many MK divergences, the comonotonic coupling is simultaneously optimal. The novel MK divergences, which can be efficiently calculated, open an array of applications in robust stochastic optimisation. We derive sharp bounds on distortion risk measures under a Bregman-Wasserstein divergence constraint, and solve for cost-efficient payoffs under benchmark constraints.

q-fin.RM↗