## Matteo Basei

Quant researcher in financial mathematics

EDF R&D, Paris

Welcome to my webpage!

I am a quant researcher and project manager at EDF R&D, with industrial and academic experience in mathematical finance and energy market modeling

## In a nutshell

Present position. Quantitative researcher and project manager at EDF R&D, working on: stochastic models and data analysis in energy markets, risk management, machine learning, derivative pricing, Python coding

Research interests. Stochastic control and games, machine learning, energy markets and derivatives

Contact. You can contact me at matteo31415 (usual symbol) gmail (dot) com

## Curriculum

• Most recent positions

• EDF R&D, Paris - Quantitative researcher (since Oct2019) and project manager (since Sep2020)

• University of California, Berkeley - Post-doc researcher (Prof. X. Guo) - Sep2017 / Aug2019

• Education

• Ph.D. in Computational Mathematics - University of Padua, Italy - Jan2013 / Dec2015

• MS in Probability and Finance - Univ. Paris VI and École Polytechnique - Sep2013 / Oct2014

• MS in Mathematics - University of Padua, Italy - Sep2010 / Jul2012

## Submitted papers

• M. Basei, X. Guo, A. Hu, Y. Zhang, Logarithmic regret for episodic continuous-time linear-quadratic reinforcement learning over a finite-time horizon, submitted [ArXiv]

We study finite-time horizon continuous-time linear-quadratic reinforcement learning problems in an episodic setting, where both the coefficients in the SDE are unknown to the controller. We propose a least-squares algorithm and establish a logarithmic regret bound of order O((ln M)(ln ln M)), with M being the number of learning episodes.

## Published papers

• M. Basei, H. Cao, X. Guo, Nonzero-sum stochastic games and mean-field games with impulse controls, to appear in Mathematics of Operations Research, 2021 [ArXiv]

We consider nonzero-sum N-player stochastic games with impulse controls. Then, we consider the limit situation $N \to \infty$, i.e., mean-field games with impulse controls. Under appropriate conditions, the MFG is an $\epsilon$-NE approximation to the N-player game, with $\epsilon=\frac{1}{\sqrt{N}}$. As an example, we propose a cash management problem.

• R. Aïd, M. Basei, H. Pham, A McKean-Vlasov approach to distributed electricity generation development, Math. Methods Oper. Res. 91 (2020), 269-310 [ArXiv] [Article]

Consumers satisfy their electricity demand by self-production (solar panels) and centralized production (energy companies). We consider the point of view of a consumer, an energy company, a social planner: we characterize the production strategies which minimize the costs and look for an equilibrium price.

• R. Aïd, M. Basei, G. Callegaro, L. Campi, T. Vargiolu, Nonzero-sum stochastic differential games with impulse controls: a verification theorem with applications, Math. Oper. Res. 45 (2020), no. 1, 205-232 [ArXiv] [Article]

We consider a general nonzero-sum impulse game with two players. The main contribution is a verification theorem which provides a suitable system of quasi-variational inequalities for the value functions. As an application, we consider a one-dimensional example and provide explicit expressions for a Nash equilibrium.

• M. Basei, Optimal price management in retail energy markets: an impulse control problem with asymptotic estimates, Math. Methods Oper. Res. 89 (2019), no. 3, 355-383 [ArXiv] [Article]

We consider a retailer who buys energy in the wholesale market, resells it to final consumers, and looks for the price strategy maximizing his profit. We formulate a suitable infinite-horizon stochastic impulse control problem, characterize an optimal price strategy, and provide asymptotic estimates for the action region.

• M. Basei, H. Pham, A weak martingale approach to linear-quadratic McKean-Vlasov stochastic control problems, J. Optim. Theory Appl. 181 (2019), no. 2, 347-382 [ArXiv] [Article]

We propose an original approach to solve linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon problems, and allow some coefficients to be stochastic. We illustrate our results through an application to the production of an exhaustible resource.

• M. Basei, A. Cesaroni, T. Vargiolu, Optimal exercise of swing contracts in energy markets: an integral constrained stochastic optimal control problem, SIAM J. Finan. Math. 5 (2014), no. 1, 581–608 [Article]

We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton–Jacobi–Bellman equation. The case of contracts with strict constraints gives rise to a control problem with nonstandard state constraints.

## Teaching

• [responsible instructor, in English] Financial engineering systems I (45 students), Spring 2019, Master of Engineering (MEng), IEOR department, University of California, Berkeley

Markov chains, Poisson and Hawkes processes, Markov decision processes (dynamic programming, value iteration, Q-learning

• [responsible instructor, in English] Introduction to financial engineering (65 students), Fall 2018, Master of Engineering (MEng), IEOR department, University of California, Berkeley

Introduction to finance (interest rates, financial instruments, arbitrage), discrete-time models (Markowitz problem, binomial model, no-arbitrage pricing), continuous-time models (stochastic calculus, martingales, Ito’s lemma, Black-Scholes model), Monte Carlo methods

• [exercises, in French] Financial mathematics (48h, 25 students), Spring 2017, Master 1 ISIFAR, Université Paris Diderot

Interest rates, financial instruments, no-arbitrage assumption, discrete-time martingales, binomial model, no-arbitrage pricing, American options