11 problems

Let $h(t,m;s)$ denote the solution of the PDE … with terminal condition $h(s,m;s)=1$. Quadratic-exponential form conjecture. The solution has the form … This ansatz is intended to…

Waiting-region threshold conjecture. There exists a function $\Gamma(x,t)$ such that

Single-exponential-mode conjecture. Either $C^{b}$ vanishes identically or $C^{l}$ vanishes identically. In particular,

Time-to-maturity dependence conjecture. The coefficient functions depend on $s$ and $t$ only through $q=t-s$:

Time-homogeneous free-boundary conjecture. The boundary and coefficient functions depend on time only through the indicated state variables:

Let $u_1\leq u_2<w_0=\infty$ be the thresholds in the collaborating business-lines model, let $M_1<\infty$ be the upper bound on the reinsurance control, and let $\pi^*_1(x)$ denot…

Affine-form conjecture. The solution of the extended HJB system has the form

Let $\xi(u,m)$ denote the value function for the minimum probability of drawdown, and let $\mathcal{H}^*_l(u)$ be the strategy specified by … Suppose the condition … holds for all…

The insurer value-function conjecture. The value function has the form

Let $u(x)$ denote the proportional reinsurance control, taking values in $[0,1]$, and let $x_0$ be a possible switching point between the interior-control regime and the full-contr…

In the impulse-control formulation, the intervention changes the reserve process by jumps; a band-type policy is described by intervention thresholds and post-intervention levels,…