Discrete asset pricing under transaction costs and model uncertainty with and without short-sale constraints

Battle Count: 174

The paper provides rigorous theoretical foundations for asset pricing under realistic market frictions (bid-ask spreads, short-sale constraints, model uncertainty). The consistent price system framework and robust supermartingale conditions are directly relevant to understanding no-arbitrage bounds in markets with transaction costs. The multi-period tree construction with conditional dual bounds informs dynamic hedging and valuation. However, the paper is purely theoretical with no empirical validation, no algorithmic implementation, and no direct trading strategy. Its relevance is foundational rather than immediately actionable for quantitative trading systems.

The theoretical constructions are mathematically sophisticated, involving convex cone duality, Farkas' lemma, backward-forward recursion on trees, and Bayes' formula for change of measure. For a finite-state implementation, the backward recursion on solvency cones and the linear programming dual construction are computationally tractable but require careful handling of conditional expectations at each node. The paper does not provide pseudocode or algorithms, so implementation would require significant mathematical translation. The finite-state assumption keeps complexity polynomial in the number of states and time steps.

The paper is purely theoretical with complete proofs. All constructions (consistent price systems, solvency cones, backward recursion, Farkas' lemma applications) are fully specified. The two-state counterexample (Example 2.1) is explicitly numerical and verifiable. No computational experiments or code are needed. The finite-state framework makes all objects explicitly computable in principle.