Can anyone tell me whether you can use the mmult(), minverse(), and mdeterm() functions on the Excel spreadsheet you get at Pearson?
I’ve been spending all this time learning how to calculate inverse matrices or stationary probabilities for Markov chains by hand. But I just found out that Excel has a handful of matrix functions. The Pearson website has a link to a ‘Spreadsheet Function List’ workbook (https://home.pearsonvue.com/Clients/Casualty-Actuarial-Society-(CAS).aspx), and those functions appear there. I’m crossing my fingers they’re genuinely available – I’d love it if someone could confirm.
If you can invert the transition probability matrix for a transient class, you could easily pull out all the time in transient state values. And if you can multiply matrices repeatedly, you could quickly bypass calculating stationary probabilities by hand by just repeatedly squaring the transition probability matrix until it converges. HECK, you could do that with gambler’s ruin problems as well without remembering that silly formula or first principles. Squaring the matrix repeatedly would converge toward ruin or winning based on any state you begin in. I’m sure there are numerous other applications.