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

Abstract

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).

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 21 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.