I have read that the utility function is usually concave. I assume this requirement arises in order to meet the diversification effect:$$f(\lambda_1c_1+\lambda_2c_2)\ge \lambda_2 f(c_1)+\lambda_2f(c_2)$$ for some $\lambda_1,\lambda_2\leq1$ and $c_1,c_2$ two assets with some payoff. An investor is happier to hold $c_1,c_2$ in a portfolio than separately.
Question: Why do we restrict $\lambda_1$,$\lambda_2$ to be less than 1? Is it not useful to require $-f$ to be sub linear so I can consider any arbitrary composition of $c_1$ and $c_2$, i.e. $\lambda_1, \lambda_2 \in \Bbb R^+$