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Long time behavior of optimal liquidation problems with semimartingale strategies and external flows

Author

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  • Xinman Cheng

    (The Hong Kong Polytechnic University)

  • Guanxing Fu

    (The Hong Kong Polytechnic University)

  • Xiaonyu Xia

    (Wenzhou University)

Abstract

In this paper, we study the long time behavior of an optimal liquidation problem with semimartingale strategies and external flows. To investigate the limit rigorously, we study the convergence of three BSDEs characterizing the value function and the optimal strategy, from finite horizon to infinite horizon. Our model includes stochastic control problems with and without discount as special cases. We find that in either case, whether the player will liquidate or not depends on the form of the external flow: the player will (not) liquidate if the intensity of the external flow is weak (strong) enough. Moreover, in the situation when the player does not liquidate in the long run, her position fluctuates around zero and we show that the trading sign is determined by that of the external flow.

Suggested Citation

  • Xinman Cheng & Guanxing Fu & Xiaonyu Xia, 2025. "Long time behavior of optimal liquidation problems with semimartingale strategies and external flows," Mathematics and Financial Economics, Springer, volume 19, number 3, December.
    • Handle: RePEc:spr:mathfi:v:19:y:2025:i:3:d:10.1007_s11579-025-00390-6
    DOI: 10.1007/s11579-025-00390-6
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