A fixed synthetic scenario · 195 kernel-checked theorems
One fixed synthetic household: $500K at 6.49%, $5K of slack each month, a 24% marginal tax rate. Prospect theory prices the gut. Kelly prices the edge. Tax theorems set the break-even at 5.803%. The scenario is fictional, and nothing here is financial advice.
Act I · Prospect theory
Kahneman and Tversky's 1992 cumulative parameter fit puts loss aversion at λ = 2.25 with curvature α = β = 0.88. The corpus proves the algebra behind the feeling: for any positive x, |v(−x)| / v(x) = λ exactly. A $1,000 loss weighs 2.25 times the same gain. The theorem does not tell you to feel less. It tells you how much you feel.
Act II · The guaranteed side
At a 24% marginal rate, itemizing drops the 6.49% nominal mortgage to 6.49% · (1 − 0.24) = 4.9324% after tax. Every extra principal dollar saves that rate with zero variance. The corpus proves the after-tax rate is weakly below nominal, and that the scenario's first-year interest clears the standard deduction, so the itemizing is real, not assumed.
Act III · The growth side
The Kelly fraction is f* = μ_excess / σ². At the scenario's 10% expected return and 15% volatility, the excess over the 6.49% mortgage is 3.51%, so f* ≈ 1.56: full Kelly says borrow and hold 156% in equities. The corpus proves f* beats every other fraction on log-growth, and it proves the discipline too: half-Kelly keeps 3/4 of the growth at 1/4 of the variance, and betting past 2f* is strictly worse than optimal.
Act IV · The synthesis
For risk aversion γ between 2 and 4, the recommended split's realized 6.8% dominates the 4.9324% after-tax mortgage rate; at γ = 3 the Merton fraction puts 52.86% of the flow in equities, about $2,643 of the $5K. The corpus keeps the other answer honest too: for loss aversion λ ≥ 2 the market's certainty equivalent falls below the guaranteed mortgage return, and the key-insight theorem records a Sharpe under 0.25 with over 1% volatility drag. The defensible default leans mortgage. The split is the compromise.
The archive is free to read. The explorer carries every theorem with its file and line. The scenario on this page is fixed and synthetic; nothing here is financial advice.