A third look at a joint probability approximation for ruin risk

This is a quick extension of the first two posts

1. The aha moment
2. a second look: Running it with different spend rates

Acknowledging that someone has probably already done this before, this third look is merely running the joint probability (net-wealth duration, being alive) process with different levels of return volatility. Check back to the other links for the main description, background info and assumptions.


Here we have:

• 60 year old 
• 4% spend rate
• 4% return[1] 
• 90/8.5 longevity mode/dispersion
• Std dev of returns is varied per below

The calibration check - ruin estimates for different levels of volatility:

Std dev.		5%	10%	15%	20%	25%	30%
Joint prob. estimate		0.021	0.138	0.258	0.379	0.484	0.562
Kolmogorov estimate		0.023	0.132	0.255	0.366	0.462	0.545

What it looks like:

And lastly, the joint prob. illustration chart for different levels of vol.

[1] maybe say 8% gross then net 3% inflation and say 1% for some combo of tax and fees.