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Buying at Support: The Entry Problem under Multi-Skew Brownian Motion

  • Jun Maeda
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Abstract

We study when to buy a share that will later be sold optimally, when the price follows a geometric multi-skew Brownian motion whose skew levels model support and resistance. The reward for buying is the exit premium of the liquidation problem solved in a companion paper. This premium is strictly r-subharmonic inside the exit continuation region, so buying is optimal only at levels where the price is pushed upward, and the entry problem reduces to a finite one whose value is an upper concave hull of finitely many points. With one support and one resistance, the optimal rule is to buy exactly at the support, in every exit regime, with an explicit value.

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Cite

BibTeXRIS
BibTeX
@misc{maeda2026buying,
  title = {{Buying at Support: The Entry Problem under Multi-Skew Brownian Motion}},
  author = {Jun Maeda},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04990},
  eprint = {2610.04990},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04990},
}
RIS
TY  - UNPB
TI  - Buying at Support: The Entry Problem under Multi-Skew Brownian Motion
AU  - Jun Maeda
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.04990
UR  - https://arxiv.org/abs/2610.04990
AB  - We study when to buy a share that will later be sold optimally, when the price follows a geometric multi-skew Brownian motion whose skew levels model support and resistance. The reward for buying is the exit premium of the liquidation problem solved in a companion paper. This premium is strictly r-subharmonic inside the exit continuation region, so buying is optimal only at levels where the price is pushed upward, and the entry problem reduces to a finite one whose value is an upper concave hull of finitely many points. With one support and one resistance, the optimal rule is to buy exactly at the support, in every exit regime, with an explicit value.
ER  -