In a nutshell

Present position. Post-doc researcher (supervisor Prof. X. Guo), University of California, Berkeley, IEOR department and TBSI institute

Research interests. Stochastic control and games, McKean-Vlasov control, energy markets and derivatives, applied probability

Contact. You can contact me at basei (usual symbol) berkeley (dot) edu

Curriculum

• For a complete CV, click here
• Positions
  • University of California, Berkeley - post-doc researcher (Prof. X. Guo) - since Sep2017
  • Université Paris Diderot, Paris - post-doc researcher (Prof. H. Pham) - Feb2016 / Jul2017
  • Gaz de France (now Engie), Paris - quantitative analyst intern - Apr / Oct2014 & Jan / Jul2015
• 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

Publications

• M. Basei, Optimal price management in retail energy markets: an impulse control problem with asymptotic estimates, to appear in Mathematical Methods of Operations Research [ArXiv]

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.

• R. Aïd, M. Basei, G. Callegaro, L. Campi, T. Vargiolu, Nonzero-sum stochastic differential games with impulse controls: a verification theorem with applications, to appear in Mathematics of Operations Research [ArXiv]

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, H. Pham, A weak martingale approach to linear-quadratic McKean-Vlasov stochastic control problems, to appear in Journal of Optimization Theory and Applications [ArXiv]

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.

Submitted papers

• M. Basei, H. Cao, X. Guo, Nonzero-sum stochastic games with impulse controls, submitted [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, The coordination of centralised and distributed generation, submitted [ArXiv]

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.

In preparation

• M. Basei, X. Guo, A. Hu, Continuous-time linear-quadratic episodic reinforcement learning, in preparation

Teaching

• [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

• [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