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Two-Sided Singular Control of an Inventory with Unknown Demand Trend
Verification Theorem and Optimal Control
Optimality of control P"0362P.
Introduction
Problem Formulation and the Separated Problem
The separated problem
The First Related Optimal Stopping Game
A Decoupling Change of Measure
Transformation of process to .
Change of measure from ¶ to QT, for some fixed T>0.
Passing to the limit as T and to the new measure Q.
The optimal control problem with state-space process (XP,) under the new measure Q.
The optimal stopping game associated to (4.8)–(4.9) under the new measure Q.
HJB Equation and Regularity of V
Verification Theorem and Optimal Control
Construction of control P"0362P for state-space process (XP"0362P,).
Transformation of controlled process (XP"0362P,) to (XP"0362P,YP"0362P).
Optimality of control P"0362P.
Refined Regularity of the Free Boundaries and their Characterization
Parabolic formulation and Lipschitz continuity of the free boundaries
Global C1-regularity of v"0362v
Integral equations for the free boundaries
Appendix A
Proof of Proposition 5.1
Proof of Lemma 7.2
Proof of Proposition 7.6
Proof of Proposition 7.8
References
Working Paper
Two-Sided Singular Control of an Inventory with Unknown Demand Trend
Place and Date of Creation
2021
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