2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125072For a game with positive profit, the optimal proportion of investment required to continue investing without borrowing is uniquely determined by an integral equation for each price. For a game with parallel translated profit, the ratio of the optimal proportion of investment to its price has some invariance properties. The optimal price of a game with parallel translated profit converges to its expectation divided by e to the riskless interest rate for a certain period.5 pagesOptimization and Control91B28 (Primary); 45G15 (Secondary)text