8 problems

Let $\bar\Lambda^{SD}$ denote the scenario-dependent aggregation function associated with scenario-dependent systemic risk measures. Consider decompositions of $\bar\Lambda^{SD}$ i…

Let $X_i$ be the payment of bank $i$, let $A_i^{\mathrm{in}}$ be its incoming-neighbor set, and let $A_j$ be the outgoing-neighbor set of bank $j$. Let $Z$ be a common shock, $Z_i$…

Let $D_n$ be the total number of defaults, let $Z/B_n$ be the common shock per bank, let $c$ be the baseline parameter, and let $\widetilde D_n$ count the individual shocks equal t…

Correlated-shock fixed-point conjecture. As $n\to\infty$,

Let $D_n$ be the total number of defaults among $n$ banks, and let $p$ be the corresponding asymptotic default probability. Default-count conjecture. The random variable $D_n$ shou…

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…

Composition conjecture. The composition of the system might also affect systemic risk.

Let $r$ denote the graph assortativity coefficient of the banking network, and let systemic susceptibility refer to the network's propensity to produce contagion cascades under sho…