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This article is cited in 11 scientific papers (total in 11 papers)
Partial observation control in an anticipating environment
B. Øksendala, A. Sulemb a University of Oslo, Centre of Mathematics for Applications
b French National Institute for Research in Computer Science and Automatic Control,
INRIA Paris - Rocquencourt Research Centre
Abstract:
A study is made of a controlled stochastic system whose state $X(t)$ at time $t$ is described by a stochastic differential equation driven by Lévy processes with filtration
$\{\mathscr F_t\}_{t\in[0,T]}$. The system is assumed to be anticipating, in the sense that the coefficients are assumed to be adapted to a filtration $\{\mathscr G_t\}_{t\geqslant0}$ with $\mathscr F_t\subseteq\mathscr G_t$ for all $t\in[0,T]$. The corresponding anticipating stochastic differential equation is interpreted in the sense of forward integrals, which naturally generalize semimartingale integrals. The admissible controls are assumed to be adapted to a filtration $\{\mathscr E_t\}_{t\in[0,T]}$ such that
$\mathscr E_t\subseteq\mathscr F_t$ for all $t\in[0,T]$. The general problem is to maximize a given performance functional of this system over all admissible controls. This is a partial observation stochastic control problem in an anticipating environment. Examples of applications include stochastic volatity models in finance, insider influenced financial markets, and stochastic control of systems with delayed noise effects. Some particular cases in finance, involving optimal portfolios with logarithmic utility, are solved explicitly.
Received: 20.06.2003
Citation:
B. Øksendal, A. Sulem, “Partial observation control in an anticipating environment”, Uspekhi Mat. Nauk, 59:2(356) (2004), 161–184; Russian Math. Surveys, 59:2 (2004), 355–375
Linking options:
https://www.mathnet.ru/eng/rm723https://doi.org/10.1070/RM2004v059n02ABEH000723 https://www.mathnet.ru/eng/rm/v59/i2/p161
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Abstract page: | 623 | Russian version PDF: | 223 | English version PDF: | 11 | References: | 66 | First page: | 2 |
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