7 problems

Let $h(t,y,z)$ be the transformed value function and let $\delta(t)$ be the free-boundary curve. In the region … consider functions $P(t,z)$ and $H(t,z)$ independent of $y$. Quadra…

Let $h(t,y,z)$ denote the transformed value function obtained from the CARA ansatz, and let $k$ be a smooth convex information-cost function. In the truncated piecewise-linear appr…

Let $V=V(t,x,y,z)$ be the value function in the CARA-normal-prior portfolio problem, with derivatives $V_x$, $V_z$, and $V_{yy}$ taken with respect to the indicated variables. Nonn…

In online portfolio selection, let FTRL denote Follow-the-Regularized-Leader and let LB-FTRL denote FTRL using the log-barrier regularizer. Van Erven et al.'s conjecture. FTRL with…

Van Erven and Koolen's conjecture. The dependence on $G$ in this regret bound may be merely an artifact of the analysis.

Let $Y$ denote the process arising in the linear-quadratic formulation, let $\widehat{X}$ be the wealth process, and let $\mathcal{A}$ be the admissible set of controls. Let…

The dynamic representation conjecture. The value function has the form