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Uspekhi Mat. Nauk, 2004, Volume 59, Issue 2(356), Pages 161–184 (Mi umn723)  

This article is cited in 8 scientific papers (total in 8 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.

DOI: https://doi.org/10.4213/rm723

Full text: PDF file (331 kB)
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English version:
Russian Mathematical Surveys, 2004, 59:2, 355–375

Bibliographic databases:

UDC: 519.218.3
MSC: 93E20, 91B28, 60H07
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

Citation in format AMSBIB
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\yr 2004
\vol 59
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\pages 161--184
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\jour Russian Math. Surveys
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\pages 355--375
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Deng P.-J., Li X.-F., Chen X.-W., “The Optimal Investment, Liability and Dividends in Insurance”, J. Oper. Res. Soc. China  crossref  isi
    2. Øksendal B., “The value of information in stochastic control and finance”, Aust. Econ. Papers, 44:4 (2005), 352–364  crossref
    3. Di Nunno G., Meyer-Brandis T., Øksendal B., Proske F., “Malliavin calculus and anticipative Ito formulae for Levy processes”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 8:2 (2005), 235–258  crossref  mathscinet  zmath  isi
    4. Di Nunno G., Meyer-Brandis T., Øksendal B., Proske F., “Optimal portfolio for an insider in a market driven by Lévy processes”, Quant. Finance, 6:1 (2006), 83–94  crossref  mathscinet  zmath  isi
    5. Øksendal B., “A universal optimal consumption rate for an insider”, Math. Finance, 16:1 (2006), 119–129  crossref  mathscinet  zmath  isi
    6. Kohatsu-Higa A., Sulem A., “Utility maximization in an insider influenced market”, Math. Finance, 16:1 (2006), 153–179  crossref  mathscinet  zmath  isi
    7. Di Nunno G., Oksendal B., “Optimal portfolio, partial information and Malliavin calculus”, Stochastics-An International Journal of Probability and Stochastic Processes, 81:3–4 (2009), 303–322  crossref  mathscinet  zmath  isi
    8. Peng X., Chen F., Wang W., “Optimal Investment and Risk Control For An Insurer With Partial Information in An Anticipating Environment”, Scand. Actuar. J., 2018, no. 10, 933–952  crossref  mathscinet  zmath  isi  scopus
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