I'm interested in the solution to the following problem:

I have initial capital $C$ which I can invest into $M$ classes of resources, each unit of a class $m_i$ matures at time $t_i$, has a return of $r_i$ and a cost $c_i$. After the asset matures it the proceeds can be re-invested. What is the optimal strategy to invest $C$ in terms of profit at time $t$ and for $t\rightarrow\infty$?

I am interested in both cases where $m_i\in\mathbb{R}^{*}$ m_i$ is in the non-negative reals and the case when $m_i\in\mathbb{N}$m_i$ is a member of the non-negative integers.

What is the field that studies this topictype of continual optimization problem?

I'm interested in the solution to the following problem:

I have initial capital $C$ which I can invest into $M$ classes of resources, each unit of a class $m_i$ matures at time $t_i$, has a return of $r_i$ and a cost $c_i$. What is the optimal strategy to invest $C$ in terms of profit at time $t$ and for $t\rightarrow\infty$?

I am interested in both cases where $m_i\in\mathbb{R}^{*}$ and $m_i\in\mathbb{N}$

What is the field that studies this topic?