Backward Stochastic Differential Equations and Optimal Control of Marked Point Processes
We study a class of backward stochastic differential equations (BSDEs) driven by a random measure or, equivalently, by a marked point process. Under appropriate assumptions we prove well-posedness and continuous dependence of the solution on the data. We next address optimal control problems for poi...
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| Veröffentlicht in: | SIAM journal on control and optimization 2013-01, Vol.51 (5), p.3592-3623 |
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| container_title | SIAM journal on control and optimization |
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| creator | Confortola, Fulvia Fuhrman, Marco |
| description | We study a class of backward stochastic differential equations (BSDEs) driven by a random measure or, equivalently, by a marked point process. Under appropriate assumptions we prove well-posedness and continuous dependence of the solution on the data. We next address optimal control problems for point processes of general non-Markovian type and show that BSDEs can be used to prove existence of an optimal control and to represent the value function. Finally we introduce a Hamilton--Jacobi--Bellman equation, also stochastic and of backward type, for this class of control problems: when the state space is finite or countable we show that it admits a unique solution which identifies the (random) value function and can be represented by means of the BSDEs introduced above. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1137/120902835 |
| format | Article |
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| ispartof | SIAM journal on control and optimization, 2013-01, Vol.51 (5), p.3592-3623 |
| issn | 0363-0129 1095-7138 |
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| source | SIAM Journals Online |
| subjects | Random variables |
| title | Backward Stochastic Differential Equations and Optimal Control of Marked Point Processes |
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