We develop the stochastic Perron's method (see e.g. arXiv: 1212.2170) in the framework of stochastic target games (arXiv: 1307.5606), in which one player tries to find a strategy such that the state process almost-surely reaches a given target no matter which action is chosen by the other...

Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) are popular risk measures from academic, industrial and regulatory perspectives. The problem of minimizing CVaR is theoretically known to be of Neyman-Pearson type binary solution. We add a constraint on expected return to investigate the...

We propose a betting strategy based on Bayesian logistic regression modeling for the probability forecasting game in the framework of game-theoretic probability by Shafer and Vovk (2001). We prove some results concerning the strong law of large numbers in the probability forecasting game with...