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Posts
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Blog Post number 4
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Blog Post number 1
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portfolio
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publications
Sur les courbes de Brody dans P^n(C)
Published in Mathematische Annalen, 2012
Nevanlinna theory and defect relations for Brody curves in projective spaces.
Recommended citation: B. F. P. Da Costa, J. Duval. "Sur les courbes de Brody dans $P^n(\mathbf C)$". Mathematische Annalen 355 (2013), no. 4, p. 1593-1600.
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Deux exemples sur la dimension moyenne d’un espace de courbes de Brody
Published in Annales de l'Institut Fourier, 2013
Mean dimension of the space of Brody curves in (a) Hopf surfaces and (b) P2 minus a line.
Recommended citation: Bernardo Freitas Paulo da Costa. "Deux exemples sur la dimension moyenne d'un espace de courbes de Brody." Annales de l'Institut Fourier. 63(6), 2013, p. 2223-2237.
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Reaction–Diffusion models: From particle systems to SDE’s
Published in Stochastic Processes and their Applications, 2019
A construction of a family of Reaction–Diffusion models that converge after scaling to the solution to a non-linear V-dimensional SDE.
Recommended citation: C. da Costa, B. F. P. da Costa, M. Jara. "Reaction–Diffusion models: From particle systems to SDE's". Stochastic Processes and their Applications 129 (2019), no. 11, p. 4411-4430.
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Stochastic Lipschitz dynamic programming
Published in Mathematical Programming, 2020
Non-convex approximation of the cost-to-go functions in multistage stochastic mixed integer linear programming.
Recommended citation: S. Ahmed, F. G. Cabral, B. F. P. da Costa. "Stochastic Lipschitz dynamic programming". Mathematical Programming, 191, 2022, 755-793.
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Dual SDDP for risk-averse multistage stochastic programs
Published in Operations Research Letters, 2023
Dual SDDP and deterministic upper bounds for risk-averse multistage stochastic programs.
Recommended citation: B. F. P. da Costa, V. Leclere. "Dual SDDP for risk-averse multistage stochastic programs". Operations Research Letters, 51(3), 2023, 332-337.
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Reaction–Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential Equations
Published in Journal of Theoretical Probability, 2023
We extend the construction of reaction–diffusion models to provide scaling limits as SDEs in infinite graphs.
Recommended citation: C. da Costa, B. Freitas Paulo da Costa, D. Valesin. "Reaction–Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential Equations". Journal of Theoretical Probability, 36(2), 2023, 1059-1087.
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Risk budgeting portfolios from simulations
Published in European Journal of Operational Research, 2023
Algorithms for building risk budgeting portfolios from simulations of returns with coherent risk measures, such as Expected Shortfall.
Recommended citation: B. Freitas Paulo da Costa, Silvana M. Pesenti, Rodrigo S. Targino. "Risk budgeting portfolios from simulations". European Journal of Operational Research, 311(3), 2023, 1040-1056.
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Boundary Conditions for Hydrothermal Operation Planning Problems: The Infinite Horizon Approach
Published in XLIII Congresso Nacional de Matemática Aplicada e Computacional, 2024
Using periodic models to improve the long-term planning of hydrothermal operation and inform expansion planning.
Recommended citation: BFP da Costa et al. "Boundary Conditions for Hydrothermal Operation Planning Problems: The Infinite Horizon Approach". XLIII Congresso Nacional de Matemática Aplicada e Computacional, Porto de Galinhas, PE, 16–20 Setembro 2024.
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Policy with guaranteed risk-adjusted performance for multistage stochastic linear problems
Published in Computational Management Science, 2024
Dual bounds and policy approximation for multistage stochastic linear problems.
Recommended citation: L Merabet, BFP da Costa, V Leclere. "Policy with guaranteed risk-adjusted performance for multistage stochastic linear problems". Computational Management Science 21 (2024), no. 2, p. 43.
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O Dilema na Alocação de Energia Firme: Vazões Totais contra Incrementais em Cascatas Hidrelétricas
Published in LVI Simpósio Brasileiro de Pesquisa Operacional, 2024
Uma discussão sobre a definição de Energia Firme de usinas hidrelétricas em cascata, do ponto de vista da teoria dos jogos.
Recommended citation: Rafael Benchimol Klausner, Joaquim Dias Garcia, Bernardo Freitas Paulo da Costa, Alexandre Street, Sérgio Granville. "O Dilema na Alocação de Energia Firme: Vazões Totais contra Incrementais em Cascatas Hidrelétricas". In: Anais do LVI Simpósio Brasileiro de Pesquisa Operacional, 2024, Fortaleza.
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talks
Using disjunctive programming to represent Risk Aversion policies
Published:
We present a disjunctive programming approach to model risk aversion in the Brazilian Energy sector, and compare its performance with the traditional risk-averse approach using risk measures. We observe a better policy, with a more realistic representation of the decision maker’s preferences, and discuss the computational aspect of its implementation.
Stochastic Lipschitz Dynamic Programming
Published:
We propose the usage of non-convex approximations for the value functions in multistage stochastic mixed-integer optimization problems. A core idea is using non-convex building blocks to approximate the value functions, generalizing the classical SDDP algorithm that uses cuts and only builds convex approximations. We explore several possibilities for obtaining such approximations, including generalized augmented duality cuts and direct Lipschitz constant estimates. We also prove that the resulting algorithm, called Stochastic Lipschitz Dynamic Programming (SLDP), converges to epsilon-optimal solutions under very reasonable assumptions.
Non-convexity measures
Published:
We introduce the concept of non-convexity measures to generalize the notion of gap for value functions. We show that they satisfy a general Jensen inequality and how they can be used to improve the convergence of Stochastic Dual Dynamic Programming algorithms in non-convex settings.
Risk Budgeting Portfolios from Simulations
Published:
We show several algorithms for constructing Risk Budgeting porfolios using only simulations. Such algorithms are especially useful when the underlying distribution is unknown, or when the risk measure does not allow for a closed-form expression. We compare the performance of the resulting portfolios with other strategies in a 14-year backtest, and show that they indeed provide stable asset allocations.
Deterministic Upper Bounds for Risk-averse Multistage Stochastic Programs
Published:
We show how to derive a dual formulation for Multistage Stochastic Programs with risk averse objectives, leading to a converging algorithm and corresponding deterministic upper bounds. This is a joint work with Vincent Leclère.
teaching
UFRJ
Regular courses, Universidade Federal do Rio de Janeiro, Instituto de Matemática, 2014
De 2014 a 2022.
FGV
Regular courses, Fundação Getulio Vargas, Escola de Matemática Aplicada, 2023
De 2023 a 2024.