Minicourse on Markowitz and Risk Budgeting portfolios
Minicourse, 19th Research in Options, Fundação Getulio Vargas, Rio de Janeiro, RJ
Talks and presentations
Deterministic Upper Bounds for Risk-averse Multistage Stochastic Programs
Conference talk, INFORMS Annual Meeting, Indianapolis, USA
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.
Risk Budgeting Portfolios from Simulations
Seminar, Decision, Algorithms and Geometry Seminar – École des Ponts, France
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.
Non-convexity measures
Seminar, CERMICS Seminar – École des Ponts, France
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.
Stochastic Lipschitz Dynamic Programming
Talk, International Conference on Stochastic Programming, NTNU, Trondheim, Norway
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.
Using disjunctive programming to represent Risk Aversion policies
Conference talk, International Symposium on Mathematical Programming, Bordeaux, France
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.