4 problems

Existence and uniqueness conjecture. These assumptions are sufficient to guarantee existence and uniqueness of a solution to the system, without requiring the loss and penalty to b…

Let $(U,X)$ be a random pair satisfying the consistency equation … where $(U_k,X_k)_{k\geq 1}$ are independent copies of $(U,X)$, $(\xi_k)_{k\geq 1}$ and $(\zeta_k)_{k\geq 1}$ are…

Dual fixed-point SDPPP conjecture. There exists a law $\mathcal{D}^\ast$ on $\mathfrak{P}^\ast$ such that a probability distribution $\mathcal{E}$ satisfies

Let $X_i$ denote the payment of bank $i$, with constants $k$, $a$, and $y$, and let $Z_i$ be independent shocks. Let $p$ denote the default probability and set $m=k+a+E(X_i)$. Asym…