On some explicitly solvable optimal stochastic control problems

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• Bujar Gashi (University of Liverpool)
• Tuesday 02 May 2023, 14:00-15:00
• Room 250, Arts Building (R16) .

If you have a question about this talk, please contact Hong Duong.

Three well-known optimal control problems for linear stochastic systems driven by a Brownian motion are: the linear-quadratic control, the risk-sensitive control, and the Merton problem. Although the optimality criteria of these problems are different (being quadratic, exponential, and power/logarithmic, respectively), a common characteristic is that they all have unique explicit solutions in a closed-form as a linear state-feedback control. In this talk, we give a summary of some recent generalisations of these problems that retain the explicit closed-form solvability. This will include: the generalised stochastic regulator that has state-dependent weights and a risk-sensitive version of it, the optimal control of a class of systems with square-root nonlinearities, and the indefinite risk-sensitive control. The optimal controls for some of these problems, although obtained in an explicit closed-form, are non-unique, of affine state-feedback form, or of a non-linear state-feedback form. The applications of these results to the optimal investment problem will also be included.

This talk is part of the Data Science and Computational Statistics Seminar series.

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• Data Science and Computational Statistics Seminar
• Room 250, Arts Building (R16)
• School of Mathematics events

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