Sizeable financial crises are rare, but not uncommon. Recent examples include the subprime crisis in the US, the 2008 Lehman-Brothers collapse and the sovereign-debt crisis in EU periphery countries. The reasons behind the emergence of such events, and also the extent of their effects on other economies are poorly understood. This PhD thesis intends to identify what can be done in order to reduce the exposure to external financial shocks and to limit financial-risk contagion. It will be investigated how learning about rare-disaster frequencies affects the allocation of inside money in models of the “I-theory of money” with investment banks. A crucial goal is to study how outside money (Central Bank money) could fix possible inside-money imbalances caused by disasters and by expectation changes. In addition, optimal Taylor rules (monetary-policy inflation or interest-rate targets) under learning about rare disasters will be investigated. This thesis will produce applied-theory models of learning about jump processes aiming to enhance our understanding of systemic financial and macroeconomic risk.