Extracting highest value in some unequal periods/time-series in R : I have two data frame: period_example (consists of ‘ Beg’, and ‘End’) and price_example (consists of ‘Date’ and ‘High’). I want the highest value of High for each Beg-End period. How to do it? Thank you. 

Here is the data:
> period_example <- data.frame(Beg = as.Date(c("2000-01-01","2000-01-04","2000-01-09")),End = as.Date(c("2000-01-03","2000-01-08","2000-01-12")))

> price_example <- data.frame(Date = seq(as.Date("2000-01-01"), as.Date("2000-01-12"),by="days"), High = c(100,105,104,103,102,106,107,108,109,110,115,114))

The result should be like this:
> result <- data.frame(Beg = as.Date(c("2000-01-01","2000-01-04","2000-01-09")),End = as.Date(c("2000-01-03","2000-01-08","2000-01-12")), High = c(105,108,115))
