FinancialRisk
FinancialRisk enumerates the five canonical risk categories that appear in the RS model of market equilibrium. Economists working inside the Recognition Science framework cite it when certifying that financial systems match configuration dimension D = 5. The declaration is a direct inductive definition that automatically derives the required type-class instances for decidability and finiteness.
claimLet $R$ be the set of financial risks. Then $R$ consists exactly of the five elements market risk, credit risk, liquidity risk, operational risk, and systemic risk.
background
The module treats financial markets as an instance of Recognition Science with five asset classes and five risk categories, both equal to the configuration dimension D. Equilibrium is defined by vanishing J-cost, J = 0, while positive J-cost signals price deviation and arbitrage opportunity. The inductive definition supplies the risk side of the certification that later enforces Fintype.card = 5 for both assets and risks.
proof idea
The declaration is a direct inductive definition that lists the five cases and derives DecidableEq, Repr, BEq, and Fintype instances automatically.
why it matters in Recognition Science
It supplies the risk enumeration required by the FinancialMarketsCert structure, which also records Jcost 1 = 0. The definition completes the D = 5 matching for risks inside the RS economics module and links to the broader forcing chain in which configuration dimension is fixed at five for markets.
scope and limits
- Does not assign magnitudes or probabilities to the listed risks.
- Does not model interactions or compounding among the five risk types.
- Does not derive the list from the J-cost functional or the Recognition Composition Law.
formal statement (Lean)
32inductive FinancialRisk where
33 | market | credit | liquidity | operational | systemic
34 deriving DecidableEq, Repr, BEq, Fintype
35