7 problems

The $G$-framework is built from a family of volatility-controlled paths, with the driving path represented by $B_t^\theta=\int_0^t\theta_s\,dW_s$ for controls…

Optimal exercise-time conjecture. The sequence of times

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…

Let $B$ be a $G$-Brownian motion on a time interval $[0,T]$, let $H^2_G(0,T)$ and $M^2_G(0,T)$ be the spaces appearing in the source, and let $G$ be the nonlinear function associat…

G-martingale representation conjecture. There exist $Z\in H_G^p(0,T)$ and $\eta\in M_G^p(0,T)$ such that

Let $G$-expectation space be equipped with the quadratic variation process $\langle B\rangle$ of the coordinate $G$-Brownian motion, and let $M^1_G(0,T)$ denote the corresponding s…

Peng's $G$-martingale decomposition conjecture. For every $\xi\in L^1_G(\Omega_T)$, there exist a process $Z$ and an increasing process $\{K_t\}$ such that