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What is an Infinite Risk?

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Infinite risk is a potential for an event or ongoing problem that has infinite impact.
As an example, the loss of our only known habitable planet due to factors such as an environment problem or war can arguably be considered an infinite impact. This can be modeled with two scenarios: one in which humans don't last forever due to loss of our habitat and one in which we somehow manage to survive to infinity.
Infinite risks have an interesting mathematical property in that they aren't affected much by probability. In fact, any non-zero probability of an infinite risk results in a probable loss of infinity no matter how small the probability becomes.
Risk = 0.1 × ∞ = ∞
Risk = 0.01 × ∞ = ∞
Risk = 0.000001 × ∞ = ∞
Risk = 0.00000000001 × ∞ = ∞
This means that infinite risks represent a large threat even if they have a very low probability of occurring. It can be demonstrated that reducing the probability of an infinite risk to zero, always has a return on investment of ∞, as long as your costs are less than ∞. For example, if you spend $1,000,000,000,000 to eliminate an infinite risk with a 0.00000001 chance of occurring your return on investment is ∞.
return on investment = ((gain – cost) / cost) * 100
= (((0.00000001*∞) - 1,000,000,000,000) / 1,000,000,000,000) * 100
= ∞
The mathematical properties of infinite risk suggest that investments to eliminate an global catastrophic risk can achieve high return on investment even if the probability of that risk is extremely low.
Overview: Infinite Risk
A non-zero probability of an infinite loss.
Infinite risk is essentially an abstract concept, much like infinity itself, that can be used to examine the far edges of a risk distribution.
Related Concepts


This is the complete list of articles we have written about risks.
AI Risk
Risk Avoidance
Brand Risk
Budget Risk
Business Risks
Change Risk
Compliance Risk
Concentration Risk
Cost Risk
Country Risk
Credit Risk
Demand Risk
Dread Risk
Economic Risk
Exchange Rates
Existential Risk
External Risk
Financial Risk
Force Majeure
Good Risk
Human Error
Risk Identification
Infinite Risk
Inflation Risk
Inherent Risk
Interest Rates
Internal Risks
Investing Risk
Legal Risk
Liquidity Risk
Model Risk
Moment Of Risk
Natural Disasters
Negative Risk
Operations Risk
Passive Risk
Personal Risk
Political Risk
Process Risk
Procurement Risk
Product Risk
Project Risk
Pure Risk
Quality Risk
Recession Risk
Risk Mitigation
Refinancing Risk
Regulatory Risk
Reputational Risk
Residual Risk
Resource Risk
Revenue Risk
Risk Appetite
Risk Aversion
Risk Examples
Risk Management
Risk Management Process
Risk Matrix
Risk Meaning
Risk Measurement
Risk Taking
Risk Tolerance
Risk Triggers
Risk vs Issue
Risk vs Opportunity
Risk vs Uncertainty
Risk-Reward Ratio
Seasonal Risk
Secondary Risk
Security Risk
Settlement Risk
Risk Sharing
Speculative Risk
Strategic Risk
Strategy Risk
Supply Risk
Systemic Risk
Tactical Risk
Taxation Risk
Technology Risk
Risk Transfer
Unforced Error
Upside Risk
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