Project CEMAPRE internal
|Title||A simple nonparametric method to estimate the expected time to cross a threshold - The continuous time case|
|Participants||João Nicolau (Principal Investigator)|
|Summary||First hitting time and especially the expected time to cross some thresholds are fundamental|
concepts in stochastic analysis, and yet they have received little attention in economics. One of
the reasons is probably the difficulty in obtaining a simple procedure to calculate, for example,
the expected time (ET) to reach a threshold. In fact, analytical results on first hitting time
problems are mostly based on stochastic processes of diffusion type or Markov chains where explicit
analytical expressions are usually available.
First hitting times are often used in mathematical finance, biology and other life sciences,
where the use of Markov chains and stochastic differential equations is more common, to study, for
example, time to extinction or default (in finance). Nonetheless, ET may also be a very useful tool
in economics as a way to discuss topics such as the speed of mean-reversion, the time to
equilibrium, the time to recovery or recession, etc. A specific example is provided in section 3.