When to Sell an Asset? – A Distribution Builder Approach

Battle Count: 132

The paper addresses the fundamental question of optimal timing for selling a single asset, which is directly relevant to quantitative trading strategies involving position liquidation. The Azéma-Yor barrier construction provides an implementable stopping rule. However, the paper is primarily theoretical and does not address execution, market microstructure, or multi-asset portfolio rebalancing. The risk-return tradeoff framework and explicit formulas for expected selling times are practically useful. The connection to Markowitz-style efficient frontiers for single-asset sale decisions offers a novel perspective for quantitative portfolio managers.

The theoretical framework requires deep understanding of Skorokhod embedding problems, scale functions of diffusions, and the Azéma-Yor construction. For the geometric Brownian motion case, the barrier function Ψ and stopping rule are explicitly computable. For general diffusions, one must compute the scale function and solve an ODE for expected stopping time. The distribution builder interface itself is a user-facing tool, but the underlying mathematical machinery (first-order stochastic dominance checks, moment conditions, barrier computations) requires significant numerical expertise. No code is provided.

The paper is purely theoretical with complete mathematical proofs. All results are derived analytically from well-established literature (Azéma-Yor, Grandits-Falkner, Pedersen-Peskir). The geometric Brownian motion case provides explicit formulas for attainability conditions, barrier functions, and expected selling times. Specific distribution families (log-normal, Pareto, Weibull, Gamma) are worked out in detail. However, no code or numerical experiments are provided for verification.