arXiv subjects

Marco Tarsia

Publications and source records attributed to Marco Tarsia.

4 recordsLinked to original sources

arXiv2026

Integrated expectile-based measures of inequality

Expectiles provide a class of asymmetric location functionals that incorporate the magnitude of deviations and admit a natural geometric interpretation. Building on their structural consistency with the convex stochastic order, this paper introduces a family of integrated expectile functionals for measuring risk, dispersion, and inequality. The proposed functionals admit analytical representations as integrals of expectiles across asymmetry levels and, for a distinguished subclass, geometric representations in terms of weighted areas of star-shaped sets encoding distributional asymmetry. This approach yields a new class of expectile-based inequality indices, constituting a natural counterpart to classical Gini-type measures while preserving desirable monotonicity and consistency properties. Empirical counterparts are derived in closed form and admit explicit decompositions over finite samples. The framework extends naturally to multivariate settings through directional expectile constructions, leading to measures capable of capturing genuinely joint forms of multivariate dispersion and inequality.

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arXiv2023

Subgame-perfect equilibrium strategies for time-inconsistent recursive stochastic control problems

We study time-inconsistent recursive stochastic control problems, i.e., for which Bellman's principle of optimality does not hold. For this class of problems classical optimal controls may fail to exist, or to be relevant in practice, and dynamic programming is not easily applicable. Therefore, the notion of optimality is defined through a game-theoretic framework by means of subgame-perfect equilibrium: we interpret our preference changes which, realistically, are inconsistent over time, as players in a game for which we want to find a Nash equilibrium. The approach followed in our work relies on the stochastic (Pontryagin) maximum principle: we adapt the classical spike variation technique to obtain a characterization of equilibrium strategies in terms of a generalized second-order Hamiltonian function defined through pairs of backward stochastic differential equations, even in the multidimensional case. The theoretical results are applied in the financial field to finite horizon investment-consumption policies with non-exponential actualization. Here the existence of non-trivial equilibrium policies is also ascertained.

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arXiv2021

Discrepancy geometry in approximate Bayesian inference: transport and risk perspectives

Approximate Bayesian Computation (ABC) replaces the evaluation of an intractable likelihood with comparisons between observed and simulated data. We develop a unified measure-theoretic framework for discrepancy-based Bayesian inference in which such comparisons are encoded through nonnegative compatibility weights. The proposed formulation provides a mathematical setting for studying both vanishing compatibility thresholds and large-sample asymptotic regimes, leading to convergence results and an asymptotic characterization of compatibility, including situations in which posterior concentration may fail. It also admits a natural variational interpretation through an entropy-regularized minimization principle and, when the discrepancy is induced by a Wasserstein distance, an intrinsic transport representation on spaces of probability measures, giving rise to risk-theoretic functionals. These results provide a unified probabilistic, asymptotic, variational, and geometric perspective on discrepancy-based Bayesian inference.

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arXiv2021

Equilibrium strategies for constrained time-inconsistent control problems

This paper addresses the issue of time inconsistency in recursive stochastic control problems, in which the forward state process evolves under the influence of an additional recursive utility system. Through an adaptation of Ekeland's variational principle, we establish necessary conditions for subgame-perfect (Nash) equilibrium strategies, formulated in terms of a Hamiltonian framework defined via coupled backward stochastic differential equations. To illustrate the scope of the results, we consider a constrained portfolio management problem with a finite deterministic horizon and non-exponential discounting, demonstrating the applicability of the proposed methodology in a financial context. The class of admissible constraints examined includes, in particular, the imposition of risk limits on the terminal wealth.

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