I do not think that recursion is helpful here, though not impossible. First step seems to come up with a proper definition of average number of trades open at the same time (What time? How to deal with inactivity?).

Maybe you can just re-sample your data like so:

• Find start time (time_start) of first trade.
• Find end time (time_end) of last trade.
• Define a suitable sample interval (interval, e.g 15s).
• From time_start to time_end in increments of interval do
  • Count the number of open trades at sample point: count[n x interval]
• Generate mean value from sampled list (maybe ignore samples with zero count).
• Alternatively: Use a sliding window and reduce further.
• Potential refinement: Ignore some of the first and last samples (transients).

Update: Instead of the synchronous sampling method suggested above, count parallel trades asynchronously at open/close times (events) - including/excluding the opened/closed trade respectively. You might weight the count with its duration (relative to observation period) to get an average value. Here, duration of count might differ from duration of given trade since it is the time span between adjacent events.

Example:

• Trade#1: open=10:10/close=11:15/duration=01:05;
• Trade#2: open=10:12/close=10:18/duration=00:06;
• Trade#3: open=10:15/close=10:26/duration=00:11;

=Asynchronous Method=                             =Sampling Method=
Time     Action      Count    Duration   Weight   Count  15s-Samples
-----------------------------------------------   -------------------
10:10    open#1        1         2         2/65     1       8
10:12    open#2        2         3         3/65     2      12
10:15    open#3        3         3         3/65     3      12
10:18    close#2       2         8         8/65     2      32
10:26    close#3       1        49        49/65     1     196
11:15    close#1       0         -          -       -       - 
-----------------------------------------------   -------------------
[download]

Observation period: 10:10-11:15 = 65 (Minutes) = 260 15s-samples
Asynchronous Method: Weighted sum (count * weight) = 82/65; Events = 6; Duration = 65; Average = 82/65 = 1.26
Sampling Method: Sum = 328; Samples = 260; Duration = 260; Average = 328/260 = 1.26
(Pardon me for leaving out the units...)

Seems, the asynchronous method is more efficient (same result, lesser computations).

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