Article1978

On the Stochastic Maximum Principle

23 citations0/0 files storedSIAM Journal on Control and Optimization

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Stochastic processes and financial applications Advanced Control Systems Optimization Optimization and Variational Analysis

Abstract

A representation of the adjoint process, which appears in a general version of the maximum principle for control systems described by Girsanov solutions of stochastic differential equations, is given in terms of the linearization of the state equation. The result is only valid when the optimal control and the coefficiencies in the state equation are smooth; however two examples show that the result can nevertheless be applied to the nonsmooth case, solving in particular the linear regulator and the “predicted miss” problems.

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References

1960On Transforming a Certain Class of Stochastic Processes by Absolutely Continuous Substitution of Measures 1972Necessary Conditions for Continuous Parameter Stochastic Optimization Problems 1970The Representation of Functionals of Brownian Motion by Stochastic Integrals 1978Functionals of Itô Processes as Stochastic Integrals 1976Full “Bang” to Reduce Predicted Miss is Optimal

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1996The maximum principle for optimal control of diffusions with non-smooth coefficients

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