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It is one of the few cases of stochastic singular control where the solution is known. For a graphical representation, the amount invested in each of the two assets can be plotted on the x - and y -axes; three diagonal lines through the origin can be drawn: the upper boundary, the Merton line and the lower boundary.
If the AFN (Additional Funds Needed) value comes out to be negative, this is actually a positive situation for the company! A negative AFN means that the company will not need external financing to support its growth. It indicates that the company has enough internal funds to support its projected sales growth. [1] The AFN equation is as follows:
Variable universal life insurance (often shortened to VUL) is a type of life insurance that builds a cash value. In a VUL, the cash value can be invested in a wide variety of separate accounts, similar to mutual funds, and the choice of which of the available separate accounts to use is entirely up to the contract owner.
The solution to Merton's theoretical model, one in which investors chose between income today and future income or capital gains, is a form of Bellman's equation. Because economic applications of dynamic programming usually result in a Bellman equation that is a difference equation , economists refer to dynamic programming as a "recursive ...
In a large class of singularly perturbed problems, the domain may be divided into two or more subdomains. In one of these, often the largest, the solution is accurately approximated by an asymptotic series [2] found by treating the problem as a regular perturbation (i.e. by setting a relatively small parameter to zero).
Originally developed for growth modelling, it allows for more flexible S-shaped curves. The function is sometimes named Richards's curve after F. J. Richards , who proposed the general form for the family of models in 1959.