Name
Title | ||
|---|---|---|
Stochastic Equations with Delay: Optimal Control via BSDEs and Regular Solutions of Hamilton-Jacobi-Bellman Equations |
Abstract | ||
|---|---|---|
We consider an Itô stochastic differential equation with delay, driven by Brownian motion, whose solution, by an appropriate reformulation, defines a Markov process $X$ with values in a space of continuous functions $\mathbf{C}$, with generator $\mathcal{L}$. We then consider a backward stochastic differential equation depending on $X$, with unknown processes $(Y,Z)$, and we study properties of the resulting system, in particular we identify the process $Z$ as a deterministic functional of $X$. We next prove that the forward-backward system provides a suitable solution to a class of parabolic partial differential equations on the space $\mathbf{C}$ driven by $\mathcal{L}$, and we apply this result to prove a characterization of the fair price and the hedging strategy for a financial market with memory effects. We also include applications to optimal stochastic control of differential equation with delay: in particular we characterize optimal controls as feedback laws in terms of the process $X$. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1137/080730354 | SIAM J. Control and Optimization |
Keywords | Field | DocType |
differential equation,optimal control,suitable solution,hamilton-jacobi-bellman equations,stochastic equations,markov process,regular solutions,resulting system,stochastic control,parabolic partial differential equation,unknown process,forward-backward system,stochastic differential equation,hamilton jacobi bellman equation,quadratic variation,memory effect,brownian motion,financial market | Differential equation,Mathematical optimization,Optimal control,Mathematical analysis,Bellman equation,Quadratic variation,Stochastic differential equation,Brownian motion,Partial differential equation,Mathematics,Stochastic control | Journal |
Volume | Issue | ISSN |
48 | 7 | Siam Journal on Control and Optimization 48 Issue: 7 (2010)
4624-4651 |
Citations | PageRank | References |
4 | 0.83 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| M. Fuhrman | 1 | 24 | 7.45 |
| Federica Masiero | 2 | 20 | 6.14 |
| Gianmario Tessitore | 3 | 35 | 13.55 |