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 Long-Term Actuarial Math Old Exam MLC Forum

#1
12-06-2018, 05:32 PM
 koudai8 SOA Join Date: Feb 2015 Posts: 23
Lee-Carter Model

The phrase "stochastic model" brings to mind models whose output are random. For example, the Cox-Ingersoll-Ross interest rate model, where outputs depend on a random error term.

For Lee-Carter model, I can't quite wrap my head around why it's considered "stochastic". To me, it seems once the parameters are properly calibrated with past data, the projection of future mortality rates are deterministic--ln(mu_xt) = alpha_x + beta_x * kappa_t.

So why is this classified as stochastic?

My thoughts: is it because in the framework, we assumed that there is an error term, although we're not actually projecting it? Or is it because kappa_t is a variable indexed by time?

Thanks.
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#2
12-06-2018, 10:07 PM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,723

Quote:
 Originally Posted by koudai8 The phrase "stochastic model" brings to mind models whose output are random. For example, the Cox-Ingersoll-Ross interest rate model, where outputs depend on a random error term. For Lee-Carter model, I can't quite wrap my head around why it's considered "stochastic". To me, it seems once the parameters are properly calibrated with past data, the projection of future mortality rates are deterministic--ln(mu_xt) = alpha_x + beta_x * kappa_t. So why is this classified as stochastic? My thoughts: is it because in the framework, we assumed that there is an error term, although we're not actually projecting it? Or is it because kappa_t is a variable indexed by time? Thanks.
It's because K_t is a Normal random variable.
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#3
12-07-2018, 02:24 AM
 cyitwei Member SOA Join Date: Nov 2015 Studying for Nothing Posts: 58

Quote:
 Originally Posted by koudai8 The phrase "stochastic model" brings to mind models whose output are random. For example, the Cox-Ingersoll-Ross interest rate model, where outputs depend on a random error term. For Lee-Carter model, I can't quite wrap my head around why it's considered "stochastic". To me, it seems once the parameters are properly calibrated with past data, the projection of future mortality rates are deterministic--ln(mu_xt) = alpha_x + beta_x * kappa_t. So why is this classified as stochastic? My thoughts: is it because in the framework, we assumed that there is an error term, although we're not actually projecting it? Or is it because kappa_t is a variable indexed by time? Thanks.

The K_t is a functional of Normal distrn.

If you look close enough, it's a random walk with a constant drift, or a AR(1) process in time series.
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 Tags lee-carter, mortality model