In this paper, we study the impact of the utility
functions on the risk averse investor’s equilibrium equity
premium in an economy with jump diffusion under an arbitrary
jump size. In other words, we provide answers to the investor’s
questions like how much compensation for having taken up
some risk is fair enough from an investment whose initial
wealth at time t = 0 is invested in a production economy
with jump diffusion under an arbitrary jump size if one is to
consume exponentially or quadratically from an accumulating
wealth among other utility functions. We considered the power,
negative exponential, square root and quadratic utility functions.
In these four risk averse utility functions considered, the
deterministic time preference function y(t) affects the optimal
consumption of the investor but it has no effect on the diffusive
and rare-events premia thereby not affecting the equilibrium
equity premium. However, the total value of an investor’s
wealth affects the optimal consumption but has no effect on
the equilibrium equity premium of the power and square
root utility functions. In case of the quadratic and negative
exponential utility functions, both the optimal consumption and
the equity premium are affected by the investor’s total wealth
value. Specifically, the negativity or positivity in the jump size
does not matter on the value of the equity premium of the
negative exponential utility function as this only depends on
the investor’s wealth value

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