The stochastic Integral w.r.t Semimartingales is defined for predictable Processes $\phi$ where $\int_{0}^T \phi_t dt < \infty$. How would I extend the Definition, when I want to integrate over $[0,\infty)$. I am trying to solve a optimal consumption Problem over a infinite time horizon. In https://openaccess.nhh.no/nhh-xmlui/bitstream/handle/11250/163833/framstad%20nils%20christian%200599.pdf?sequence=1 on Page 5 the admissible Controls are just required to be predictable.
2026-03-27 05:36:33.1774589793
Stochastic Integrals over infinite time horizon
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