# Maximin utility function

If someone has the attitude that they want to maximize their worst possible outcome (so they are maximally risk-averse), what does the utility function for that look like? Can this attitude be expressed as a utility function?

Maybe as a function defined by a limit?

You can simply apply what you know about perfect complements. If we have $$C_i$$ for $$i=1,2,...,n$$, where $$C_i$$ is consumption in the $$i$$th state of the world, each state of the world occuring with some probability, the utility function $$U=\min\{C_1,C_2,...,C_n\}$$ will ensure that the consumer will choose to have equal consumption in every state of the world.