2025/12/11 by Aditya Guha Roy, Yuval Peres, Roy, Aditya Guha +5
Mathematics · Decision Sciences · Economics, Econometrics and Finance · #Probability and Statistical Research #Advanced Bandit Algorithms Research #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2512.10754
A gambler with an initial fortune x starts by betting a dollar, then doubles the bet after every win and halves the bet after every loss. Let p∈ (0,1) be the probability of winning for each round. We show that the gambler survives with positive probability if and only if p < 1/2 and x > 2. Moreover, the ruin probability is increasing and real-analytic in p, but a singular, Hölder continuous function of x.