# Optimal control of semi-Markov processes with a backward stochastic differential equations approach

@article{Bandini2017OptimalCO, title={Optimal control of semi-Markov processes with a backward stochastic differential equations approach}, author={Elena Bandini and F. Confortola}, journal={Mathematics of Control, Signals, and Systems}, year={2017}, volume={29}, pages={1-35} }

In the present work, we employ backward stochastic differential equations (BSDEs) to study the optimal control problem of semi-Markov processes on a finite horizon, with general state and action spaces. More precisely, we prove that the value function and the optimal control law can be represented by means of the solution of a class of BSDEs driven by a semi-Markov process or, equivalently, by the associated random measure. We also introduce a suitable Hamilton–Jacobi–Bellman (HJB) equation… Expand

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#### References

SHOWING 1-10 OF 85 REFERENCES

Backward Stochastic Differential Equations and Optimal Control of Marked Point Processes

- Mathematics, Computer Science
- SIAM J. Control. Optim.
- 2013

Constrained BSDEs representation of the value function in optimal control of pure jump Markov processes

- Mathematics
- 2015

Backward stochastic differential equations associated to jump Markov processes and applications

- Mathematics
- 2013

$$L^p$$Lp solution of backward stochastic differential equations driven by a marked point process

- Mathematics, Computer Science
- Math. Control. Signals Syst.
- 2019

A numerical algorithm for fully nonlinear HJB equations: An approach by control randomization

- Mathematics, Computer Science
- Monte Carlo Methods Appl.
- 2014