Journal
APPLIED MATHEMATICS AND OPTIMIZATION
Volume 85, Issue 3, Pages -Publisher
SPRINGER
DOI: 10.1007/s00245-022-09848-1
Keywords
Stochastic maximum principle; Control-dependent terminal time; Optimal liquidation; Variational analysis; Backwards stochastic differential equations
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Funding
- EPSRC (UK) Grant [EP/V008331/1]
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In this paper, we study a general optimal liquidation problem with a control-dependent stopping time and prove a new stochastic maximum principle. Through a simple example, we find that the optimal solution satisfies the stochastic maximum principle in this paper but fails the standard stochastic maximum principle in previous literature.
In this paper we study a general optimal liquidation problem with a control-dependent stopping time which is the first time the stock holding becomes zero or a fixed terminal time, whichever comes first. We prove a stochastic maximum principle (SMP) which is markedly different in its Hamiltonian condition from that of the standard SMP with fixed terminal time. We present a simple example in which the optimal solution satisfies the SMP in this paper but fails the standard SMP in the literature.
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