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

Battle Count: 53

Highly relevant for strategies that exploit mean reversion around technical levels (support/resistance). It provides a rigorous mathematical foundation for the 'buy at support' heuristic, proving it is optimal under specific stochastic assumptions and providing explicit entry rules.

The theoretical derivation is complex, involving advanced stochastic calculus (Itô-Tanaka formula, local times, concave hulls). However, the resulting trading rules are simple (buy at specific price levels) and can be implemented with moderate complexity once the exit problem parameters are calibrated.

The paper provides explicit formulas for the optimal entry rules and values in specific regimes (one support/resistance, two supports). Appendix A includes a numerical check using brute-force computation on a grid, confirming the analytical results. Parameters for the numerical check are provided.