An introduction to excursion risk through discrete-time excursions

In this paper, we attempt to provide an elementary introduction to the excursion risk theory by constructing a discrete-time analogue. The excursion risk theory is a theory of calculating risks in investments that use mean-reverting trading signals. We consider the case where the trading signal is a simple symmetric random walk (RW) and use the excursions of them to compute several quantities of risks in the investments. It may be said that this paper gives one way of applying the excursion theory of RWs that mathematicians have been studying for a long time to mathematical finance.