7 problems

Constant-barrier conjecture. If the optimal strategy is of constant-barrier type, then the value function should have the form

HJB–SMP connection conjecture. The two different primal-dual formulations are connected: the Lions derivative of the HJB dual optimizer, evaluated along the optimal state process,…

Let $V(t,x)$ be the value function of the linear-quadratic stochastic control problem, with state dimension $d$ and time-dependent coefficients. Introduce a symmetric matrix-valued…

Let $v$ be the value function of the debt-smoothing problem in the simplified stochastic-control model. Twice differentiability conjecture. The value function $v$ is twice continuo…

Let $X_T$ be the set of states reachable by solutions of … from admissible initial data and forcings in $\mathcal{E}$ during some time $0\leq t^*\leq T$. Assume that $V$ solves the…

Let $\mathcal{I}$ be the intervention region, let $\mathcal{L}_X$ be the infinitesimal generator of the exchange-rate process $X$, let $r$ be the discount rate, let $h$ be the runn…

Weak-solution conjecture. If the infimum of the family $\\{\mu^{\sigma}\\}$ indexed by $\sigma$ vanishes, then $(u,\psi)$ should be a weak solution of the fully nonlinear stochasti…