## Matteo Basei

Post-doc researcher in financial mathematics

**University of California, Berkeley **

Welcome to my webpage!

I am a post-doc researcher at UC Berkeley, with academic and industrial experience in stochastic control problems applied to mathematical finance and energy markets

## 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
- post-doc researcher (Prof. X. Guo) - since Sep2017__University of California, Berkeley__- post-doc researcher (Prof. H. Pham) - Feb2016 / Jul2017__Université Paris Diderot, Paris__- quantitative analyst intern - Apr / Oct2014 & Jan / Jul2015__Gaz de France (now Engie), Paris__

- Education
- University of Padua, Italy - Jan2013 / Dec2015__Ph.D. in Computational Mathematics____MS in Probability and Finance__- University of Padua, Italy - Sep2010 / Jul2012__MS in Mathematics__

## Publications

- M. Basei,
, to appear in__Optimal price management in retail energy markets: an impulse control problem with asymptotic estimates__*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,
to appear in__Nonzero-sum stochastic differential games with impulse controls: a verification theorem with applications__,*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,
to appear in__A weak martingale approach to linear-quadratic McKean-Vlasov stochastic control problems__,*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,
SIAM J. Finan. Math. 5 (2014), no. 1, 581–608 [Article],__Optimal exercise of swing contracts in energy markets: an integral constrained stochastic optimal control problem__

*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,
, submitted [ArXiv]__Nonzero-sum stochastic games with impulse controls__

*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,
, submitted [ArXiv]__The coordination of centralised and distributed generation__

*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,
, in preparation__Continuous-time linear-quadratic episodic reinforcement learning__

## Teaching

- [instructor, in English]
__Financial engineering systems I__

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

- [instructor, in English]
__Introduction to financial engineering__

*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]
(48h, 25 students), Spring 2017, Master 1 ISIFAR, Université Paris Diderot__Financial mathematics__

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