Stochastic Control in Discrete and Continuous Time by Atle Seierstad

Author:Atle Seierstad
Language: eng
Format: epub
Publisher: Springer US, Boston, MA

(3.56)

In case of (3.52), this condition often follows more or less automatically.

The following maximum principle will normally hold as a necessary condition for optimality. The assumptions on subsequent to (3.48) and to Theorem 3.8 are again postulated.

Theorem 3.22 (Necessary conditions, end constrained case, ). Let , be an optimal pair in the end constrained problem ( 3.15 )–( 3.17 ), ( 3.47 ), ( 3.48 ), ( 3.49 ), ( 3.50 ), ( 3.53 ), bounded. Assume ( 3.56 ). Then Theorem 3.8 holds with two modification: The transversality condition ( 3.24 ) on is changed to the following one: There exist a number and multipliers , , such that ( 3.54 ) holds for , replaced by , , , , . Moreover, in ( 3.22 )–( 3.23 ), , , and are replaced by , , and , respectively. Furthermore,

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