2 problems

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Existence of a strictly positive generalised supermartingale vanishing before a finite random time
Existence conjecture. There exists such a process $Y$ and a finite random time $\tau<\infty$ such that
Conjectureopenstochastic-processes supermartingalesarXiv posted 2 days ago
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Doob–Meyer-type decomposition conjecture for G-supermartingales
Let $Y$ be a $G$ -supermartingale on a time interval $[0,T]$ . Let $B$ denote the $G$ -Brownian motion, let $Z$ be an integrand for which the stochastic integral is defined, let $K$ b…
Conjectureopeng-expectation stochastic-processes supermartingalesarXiv posted 2 days ago

Existence of a strictly positive generalised supermartingale vanishing before a finite random time