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Portfolio Selection with Transaction Costs
TLDR
It is shown that the optimal buying and selling policies are the local times of the two-dimensional process of bank and stock holdings at the boundaries of a wedge-shaped region which is determined by the solution of a nonlinear free boundary problem. Expand
Dynamic Programming Conditions for Partially Observable Stochastic Systems
In this paper necessary and sufficient conditions for optimality are derived for systems described by stochastic differential equations with control based on partial observations. The solution of theExpand
Impulse control of piecewise-deterministic processes
  • O. Costa, M. Davis
  • Computer Science, Mathematics
  • Math. Control. Signals Syst.
  • 1 September 1989
TLDR
A numerical technique for computing optimal impulse controls for P.D.P.s. under general conditions is presented and it is shown that iteration of the single-jump-or-intervention operator generates a sequence of functions converging to the value function of the problem. Expand
Pathwise Non-Linear Filtering
This paper concerns the nonlinear filtering problem of calculating recursively estimates E[f(xt)ys,0≤s≤t] where xt is a Markov process and yt is a real-valued “observation process” given by $$dy_tExpand
Approximations for optimal stopping of a piecewise-deterministic process
  • O. Costa, M. Davis
  • Computer Science, Mathematics
  • Math. Control. Signals Syst.
  • 1 June 1988
TLDR
This paper deals with approximation techniques for the optimal stopping of a piecewise-deterministic Markov process, and builds ε-optimal stopping times for the original problem using the payoff function of the discretized process. Expand
Recursive order estimation of stochastic control systems
The predictive least squares criterion for order estimation is combined with an adaptive control strategy minimizing a quadratic cost and applied to multidimensional ARX systems. It is then shownExpand
The general point process disorder problem (Corresp.)
An explicit solution is given of the nonlinear filtering problem of estimating the time of "disorder" of a counting process of very general type.
Optimal consumption and exploration: A case studyin piecewise‐deterministic Markov modelling
TLDR
In this paper, it is clearly shown how one can apply the PDP optimal control theory to the optimal consumption and exploration of non‐renewable resources under uncertain exploration. Expand
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