How to combine multiple probability distributions created through convolution - aligning x-axis

I'm simulating event losses with Monte Carlo simulation but I'm having trouble aggregating multiple event losses, specifically with aligning losses to add probabilities.

I'm using Monte Carlo to estimate the probability distribution from one event (differentiating the ECDF to get the PDF). My probability distributions are continuous (from theory) but obviously, I have a discrete approximation to them. I'm convolving my distribution estimate with itself to get the loss distribution due to two events, three events and so on.

In some cases, the distribution from one, two, or more events will overlap. But the 'x' values don't always align and I'm not sure how to add the probabilities when the x values don't align.

Here's an example.

• For a single event, the minimum loss (minimum x) might be €11, the maximum (x) might be €101, with a (x) step of €2, So I have probabilities at (x values of) €11, €13, €15...

• For two events from the convolution, the range is €22 to €202 with a step of €2. So I have probabilities at (x values of) €22, €24, €26...

The problem is, the x values don't align so I can't 'just' add the probabilities at the same x values. How can I align the x values so I can add the probabilities?

I've thought of various ways of aligning the x values, but none seem good:

• Increasing the number of steps (but I'm worried about computation time).
• Playing around with the minimum and maximum values, but I'm concerned with correctly representing distributions with a 'cliff edge' (if the distribution has a sharp drop off at €20 and I change the minimum to €18 with a step of €4, I'll miss the edge).
• Some form of interpolation, but I'm concerned about accuracy.

I'm a bit stumped about the way forward.

In the end, I used interpolation. The convolution gives "low" values at the boundaries (think CLT). Testing showed the interpolation worked well under a range of initial distributions.