# UMA Home page for Athena Picarelli

Picarelli

Athena

OC team

était :

Ph.D. 2015

## Research activities

The formulation of optimal control problems involving realistic models typically involves constraints on control and state variables, to take account of a target to be reached, mechanical or thermal constraints, obstacles, etc.
When constraints are present and when, as is often the case, rather severe controllability conditions are not satisfied, it is known that the value function may be discontinuous and these discontinuities pose some well-known issue in the characterization of the value function as unique viscosity solution of a suitable Hmilton-Jacobi equation.
Aim of my research is to provide a rigorous mathematical formalism that leads to a computation of the value function (or an other object of interest) also in absence of controllability assumption.
Main topics of interest: First and second order Hamilton-Jacobi-Bellman equations,
stochastic optimal control, viscosity solutions, numerical methods for partial differential equations.

## Teaching activities

TP for the course "Numerical methods for partial differential equations in finance".

## Publications

### Papers in peer-reviewed journals

#### 2018

**Infinite Horizon Stochastic Optimal Control Problems with Running Maximum Cost**

, and

SIAM J. Control Optim., vol. 56(5), pp. 3296--3319, 2018

#### 2016

**State-constrained stochastic optimal control problems via reachability approach**

, and

SIAM Journal on Control and Optimization, vol. 54 (5), pp. 2568–2593, 2016

#### 2015

**Dynamic programming and error estimates for stochastic control problems with maximum cost**

, and

Applied Mathematics and Optimization (AMO, Springer), vol. 71(1), pp. 125--163, 2015**Zubov’s method for controlled diffusions with state constraints**

and

Nonlinear Differential Equations and Applications, vol. 22 (6), pp. 1765–1799, Springer Verlag, 2015

#### 2012

**A patchy dynamic programming scheme for a class of Hamilton-Jacobi-Bellman equation**

, , and

SIAM J. Scientific Computing, vol. 34 (5), pp. A2625-A2649, 2012

### International conference with proceedings

#### 2012

**Reachability for state constrained stochastic control problems**

and

MTNS, jul, 2012

### Conference without proceedings

#### 2013

**New approach for stochastic target problems with state constraints**

ICCOPT, jul, 2013

### Doctoral these

#### 2015

**On some stochastic control problems with state constraints**

Ecole doctorale de l'Ecole polytechnique ED 447, apr, 2015