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Risk Aversion and a Calculus for Finitely Generated Piecewise Linear Functions: A Calculus that Economists Ought to Develop?

In this note we propose a calculus for piece-wise linear functions, in order to obtain derivatives and second derivatives at points where the function is not differentiable. Such derivatives can be used to calculate coefficients of risk aversion at initial wealth for piece-wise linear utility functions for gains, which display loss aversion-and hence non differentiability at zero gains.