Work

Optimal Control of Stochastic Delay Differential Equations and Applications to Path-Dependent Financial and Economic Models

Year: 2024

Type: article

Abstract: . In this manuscript we consider a class of optimal control problems of stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we characterize the value function of the problem as the unique viscosity solution of the associated infinite-dimensional Hamilton-Jacobi-Bellman equation. Finally, we prove a [Formula: see text]-partial regularity of the value function. We apply these results to path dependent financial and economic problems (Merton-like portfolio problem and optimal advertising).

Source: SIAM Journal on Control and Optimization

DOI: 10.1137/23m1553960

Authors: Filippo De Feo, Salvatore Federico, Andrzej Święch

Institutions: Politecnico di Milano, University of Bologna, Georgia Institute of Technology

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Ministero dell’Istruzione, dell’Università e della Ricerca

Awards: The Time-Space Evolution of Economic Activities: Mathematical Models and Empirical Applications, G873741537