On exit times of multivariate random walk with some applications to finance

Abstract

This paper analyzes multivariate delayed random walk processes and multivariate Poisson processes and presents some applications to the stock market. When trading with stock options or having, a stock portfolio (including ones by mutual funds), we are interested in various parameters, such as exit times and stock exit price values when the stock drops or when it exceeds a specified price, or even one trade ahead of the time when an exit would occur. We obtain closed form functionals of the named random parameters. We also present an example of a random walk embedded in a multivariate Poisson process.