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Economic hysteresis effects and hitting time densities for CIR diffusions

Using the so-called mean-reverting square-root process of Cox et al. (1985b) we generalize the work of Dias and Shackleton (2005) by introducing the mean reversion feature into the economic hysteresis analysis under stochastic interest rates and show that such issue highlights a tendency for a widening effect on the range of inaction, though both thresholds have risen when compared with the no mean-reverting case. In addition, using the work of Linetsky (2004) we compute the hitting time densities in order to have an idea of how long does it take for a current interest rate to revert and hit the investment thresholds that would induce idle firms to invest.