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Old 12-06-2018, 05:32 PM
koudai8 koudai8 is offline
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Default 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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Old 12-06-2018, 10:07 PM
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Jim Daniel Jim Daniel is offline
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Originally Posted by koudai8 View Post
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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Old 12-07-2018, 02:24 AM
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cyitwei cyitwei is offline
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Quote:
Originally Posted by koudai8 View Post
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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