Optimal exit strategies of CPT gamblers in unfair gambles

Battle Count: 91

The paper provides important behavioral insights into optimal exit timing under loss aversion and probability distortion, which are directly relevant to trading strategy design. The finding that CPT gamblers are less loss-tolerant and exit earlier in unfavorable conditions mirrors real trading behavior. However, the paper is purely theoretical with no direct algorithmic trading implementation. The Skorokhod embedding technique and the characterization of optimal exit distributions could inform behavioral trading models. The comparison between fair and unfair game strategies provides intuition for how adverse market conditions affect behavioral traders' exit decisions.

The mathematical machinery is highly sophisticated: geometric transformation of super-martingales to martingales, Skorokhod embedding theorem for asymmetric random walks, explicit construction of randomized Azéma-Yor stopping times, and infinite-dimensional linear programming. The analytical solutions require careful handling of piece-wise power utility functions and multiple parameter regimes. Recovering stopping strategies from optimal distributions involves path-dependent, randomized decision rules. However, for the specific parameterization studied, the formulas are explicit and computable.

The paper provides complete analytical solutions for piece-wise power utility and power probability distortion functions, with explicit formulas for optimal distributions and stopping strategies. Numerical examples with specific parameter values (α+=0.6, δ+=0.7, α-=0.8, δ-=0.7, λ=1.05) are given. All proofs are included in the appendix. However, no code or computational scripts are provided for reproducing the numerical illustrations.