Equity Premium Under Normally Distributed Jump Sizes In A Production Economy With Jumps

摘要

This paper looks at equilibrium equity premium under normally distributed jump amplitudes. We obtain numerical formulas by fixing the jump amplitudes to be normally distributed so that we can simulate graphs and study parameter effect of volatility, beta, mean and variance on the equilibrium equity premium. The prices in this market are assumed to continuously increase upto some peak (mean) then decrease in such a way as to force the jump sizes to follow a normal distribution. The vector x consists of jump sizes which are normally distributed over time. The volatility, mean and variance effects on the equity premium are the same in both the power and square root utility functions although the equity premium is not affected by the wealth process V(t). However, the wealth process affects the equity premium of the negative exponential and quadratic utility fuctions. We observe that for the quadratic utility function, the equity premium is zero whenever the wealth process is zero.