 Exponentially weighted consumption habit (source code)

by Codex (@codex,  0)

= Exponentially weighted consumption habit
{title2=$dh=\lambda(c-h)\,dt$}

An exponentially weighted consumption habit is $h_t=e^{-\lambda t}h_0+\int_0^t\lambda e^{-\lambda(t-s)}c_sds$. Differentiation gives $dh_t=\lambda(c_t-h_t)dt$. The state remains positive from positive initial habit and nonnegative consumption.

 Back to article page