Topic | People | Description | |
---|---|---|---|
Hamilton-Jacobi theories, including dynamic programming (see MSC classification) | |||
MSC 49L20 - Dynamic programming method |
Athena Picarelli |
An optimal control problem is defined starting from a dynamics, a set of controls acting on this dynamics and a cost (or gain), functional of the control and the associated dynamics. The objective is to minimize (or maximize) this cost (or gain). The value function (function of the initial time and position) is defined as the optimal value, i.e. the minimum (or maximum) value of the cost (or gain), associated to the problem. I study optimal control problems for which the dynamics is given by a stochastic differential equation. By the dynamic programming approach the value function can be characterized as the solution (in the weak viscosity sense) of a partial differential equation called the Hamilton-Jacobi-Bellman equation. | |
Numerical methods (see MSC classification) | |||
MSC 49M37 - Methods of nonlinear programming type |
Alberto Peretti Alberto Roveda |
Methods for solving constrained and unconstrained problems with non-linear functions. This includes the Gradient type methods, Method of conjugate gradient, Newton-type methods, Near-Newton methods, Penalization methods and Interior Point methods. It also covers differentiable and non-differentiable case study, Multi-objective optimization and numerical experimentation of the mentioned methods on test problems and application to real problems. | |
Data Collection and Data Estimation Methodology ; Computer Programs (see JEL classification) | |||
JEL C80 - General |
Francesco Andreoli |
Implementazione e sviluppo software per l'analisi statistica ed econometrica, per il trattamento dati e per la rappresentazione grafica. | |
Econometric and Statistical Methods and Methodology: General (see JEL classification) | |||
JEL C12 - Hypothesis Testing: General |
Cecilia Mancini Francesca Rossi |
Hypotesis testing to detect spatial correlation and to assess whether models are correctly specified, development of analytical corrections to improve tests' performance in finite samples. | |
JEL C13 - Estimation: General |
Cecilia Mancini Marco Minozzo |
Development and estimation of statistical models in finance, and for economic and social data; computationally intensive Monte Carlo estimation algorithms such as Monte Carlo EM and sequential Monte Carlo. | |
JEL C14 - Semiparametric and Nonparametric Methods: General |
Cecilia Mancini |
Stime dei coefficienti di semimartingale con salti definite a tempi continui ma osservate a tempi discreti. | |
JEL C15 - Statistical Simulation Methods: General |
Marco Minozzo Francesca Rossi |
Computer intensive estimation methods based on Monte Carlo simulations, bootstrap and indirect inference. Also includes machine learning, and development of statistical software for the analysis of economic phenomena. | |
JEL C18 - Methodological Issues: General |
Francesco Andreoli Eleonora Matteazzi Francesca Rossi |
Derivation of properties of estimators and test statistics in large samples and their analytical corrections for small/medium samples. | |
Econometric Modeling (see JEL classification) | |||
JEL C51 - Model Construction and Estimation |
Cecilia Mancini |
Modellizzazione dei (possibili) salti nei prezzi di titoli finanziari, osservati in modo discreto. | |
JEL C52 - Model Evaluation, Validation, and Selection |
Cecilia Mancini |
Stima, diagnostica e selezione di modelli per i salti nelle traiettorie dei prezzi di titoli finanziari, date osservazioni discrete. | |
JEL C58 - Financial Econometrics |
Diego Lubian Cecilia Mancini Roberto Renò |
Covers studies related to econometric modeling of financial markets. Analysis of econometric models with continuous time and its applications in finance. Robust estimates for volatility models of financial returns. | |
Mathematical Methods; Programming Models; Mathematical and Simulation Modeling (see JEL classification) | |||
JEL C61 - Optimization Techniques; Programming Models; Dynamic Analysis |
Bruno Giacomello Alessandro Gnoatto Cecilia Mancini Alberto Peretti Paolo Pertile Alberto Roveda |
Covers theory and methods for optimization problems. Linear programming and mathematical programming. Vector optimization and duality models. Economic applications to the problems of optimal investment choices under conditions of uncertainty and portfolio optimization. Estimation of the parameters of financial models including a risk-neutral assumption and calibration of the models. Stochastic optimization for finding estimators of the volatility of a semimartingale with jumps. | |
Single Equation Models; Single Variables (see JEL classification) | |||
JEL C21 - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions |
Francesca Rossi |
Inference for spatial data, teoretical analysis of the models known as spatial autoregressions and their application in empirical settings. | |
JEL C22 - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Models; Diffusion Processes |
Diego Lubian |
Estimation, inference and forecasting in time series models. Applications to financial markets. | |
JEL C23 - Models with Panel Data; Longitudinal Data; Spatial Time Series |
Alessandro Bucciol |
Panel data analysis: estimation and evaluation of static and dynamic models for microeconomic data. Applications in the fields of industrial and health economics, behavioral economics, environmental economics and consumption and saving decisions. | |
JEL C25 - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions |
Alessandro Bucciol |
Empirical and theoretical analysis of models for limited dependent variable (binary variable, count data, truncated and censored samples). With applications in the fields of environmental economics, industrial and health economics, consumption and saving decisions. | |
Mathematical programming, optimization and variational techniques (see MSC classification) | |||
MSC 65K05 - Mathematical programming methods |
Alberto Peretti |
General and numerical methods for the solution of the problem of finding the maximum/minimum of a scalar function with some equality/inequality constraints. In addition to the classical techniques that assume first and second differentiability of the functions, the case of non differentiable functions is also considered. | |
Partial differential equations, initial value and time-dependent initial- boundary value problems (see MSC classification) | |||
MSC 65M06 - Finite di erence methods |
Athena Picarelli |
Only in very few cases Hamilton-Jacobi-Bellman equations admit an explicit solution. It becomes then fundamental the numerical approximation of the solution. Numerical methods for partial differential equations are basically divided in: finite elements methods and finite difference methods. The latter are based on a Taylor approximation of derivatives. They are quite simple and intuitive methods for which a complete convergence analysis in the class of solutions of the equation in the viscosity sense is available. | |
MSC 65M15 - Error bounds |
Athena Picarelli |
Defined a numerical approximation scheme for a partial differential equation and proved its convergence, it is also interesting to provide error estimates. For classical solutions of elliptic and parabolic equation this can be obtained by quite standard techniques. However, in the particular case of viscosity solutions specific analytic regularization techniques have to be applied. | |
Probabilistic methods, simulation and stochastic differential equations (see MSC classification) | |||
MSC 65C05 - Monte Carlo methods |
Bruno Giacomello Alessandro Gnoatto Marco Minozzo |
Monte Carlo methods for estimating and predicting dynamic models, such as Markov chain Monte Carlo, particle filters and sequential Monte Carlo. Applications of these methods to economic and financial field. In particular, applications for the numerical solution of stochastic differential equations forward-backward. Also covers Longstaff-Schwartz regression methods for the solution of Snell envelopes and applications in the counterparty risk field. | |
Mathematical programming (see MSC classification) | |||
MSC 90C05 - Linear programming |
Alberto Peretti |
Methods and numerical algorithms for the solution of a linear programming problem, that is a mathematical programming problem where the functions are assumed to be linear. The simplex method and its generalizations. | |
MSC 90C30 - Nonlinear programming |
Alberto Peretti |
Methods and numerical algorithms for the solution of a mathematical programming problem where the functions are specifically assumed to be non linear. | |
MSC 90C46 - Optimality conditions, duality |
Alberto Peretti |
Optimality conditions for constrained and unconstrained extremum problems: sufficient and necessary conditions in the case of differentiable and non-differentiable functions. Image Space Analysis: sufficient and necessary optimality conditions for not convex and / or non-differentiable problems. Regularity conditions and constraint qualifications for scalar and vector optimization problems. | |
Parabolic equations and systems (see MSC classification) | |||
MSC 35K61 - Nonlinear initial-boundary value problems for nonlinear parabolic equations |
Athena Picarelli |
The study of parabolic equations is related to evolutive diffusion problems. Hamilton-Jacobi-Bellman equations are fully nonlinear possibly degenerate equations belonging to this class and arise in the study of stochastic optimal control problems. Fixed suitable initial and boundary conditions, I’m interested in the study of existence and uniqueness of solutions, their regularity and numerical approximation. | |
Stochastic analysis (see MSC classification) | |||
MSC 60H10 - Stochastic ordinary differential equations |
Alessandro Gnoatto |
Analysis of continuous time stochastic processes. Applications of stochastic differential equations of forward and backword type with jumps to problems of financial pricing and optimal control. | |
MSC 60H30 - Applications of stochastic analysis |
Maria Flora Bruno Giacomello Alessandro Gnoatto |
Applications of continuous-time stochastic processes in economics and finance. Analysis of pricing problems and contingent claims. Studies of problems of risk management and applications of measures of risk. | |
MSC 60H35 - Computational methods for stochastic equations |
Alessandro Gnoatto |
Probabilistic computational methods: recursive marginal quantization and Fourier-quantization. Exposure estimation in models featuring counterparty risk. | |
Applications (see MSC classification) | |||
MSC 62P05 - Applications to actuarial sciences and financial mathematics |
Bruno Giacomello Marco Minozzo |
Risk modelling in insurance and finance, in particular credit risk with the development of credit scoring models and algorithms; calibration of the probabilities of defaults; market segmentation. | |
Inference from stochastic processes (see MSC classification) | |||
MSC 62M10 - Time series, auto-correlation, regression, etc. |
Marco Minozzo |
Modelling and analysis (data science) of univariate and multivariate time series, equally or unequally spaced, including the use of models with latent factors and for skewed data; machine learning methods for the analysis of large collections of time series. | |
MSC 62M20 - Prediction; filtering |
Marco Minozzo |
Forecasting and filtering techniques of the signal such as, for instance, the Kalman filter; prediction, smoothing and filtering techniques based on Monte Carlo simulation, such as particle filtering and sequential Monte Carlo. | |
Multivariate analysis (see MSC classification) | |||
MSC 62H11 - Directional data; spatial statistics |
Marco Minozzo |
Modelling and analysis (data science) of areal and georeferenced data, both univariate and multivariate, with the use of Gaussian and non-Gaussian models (for discrete or skewed data, etc.); development of spatial models with latent factors; modelling of directional data. | |
Nonparametric inference (see MSC classification) | |||
MSC 62G20 - Asymptotic properties |
Catia Scricciolo |
Analysis of likelihood-based procedures: - consistency and rates of convergence of nonparametric maximum likelihood estimators in Hellinger distance; - theory of frequentist asymptotic properties for nonparametric Bayes procedures, including general contraction rate results for posterior distributions, adaptive estimation and coverage properties of nonparametric credible sets. | |
Parametric inference (see MSC classification) | |||
MSC 62F15 - Bayesian inference |
Catia Scricciolo |
Bayesian theory of function estimation in nonparametric statistical models, including the study of credible sets to provide a data-driven quantification of the uncertainty for point estimators. Analysis also covers inverse problems, such as deconvolution, wherein the object of interest has to be recovered from indirect noisy observations. |
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