Optimizing Optimization: The Next Generation of Optimization Applications and Theory (Quantitative Finance)

80 Optimizing Optimization

Tobin eloquently encapsulates the constraint, both practical and fiduciary,
that governs organizations that expect or intend to perpetuate through the
ages. Such Foundations we shall define as “ infinitely lived. ” Implicit in the
decision to limit present consumption for future consumption is the assump-
tion that the future good derived from the endowment is roughly equal on
some measure of benefit to the good derived in the present. What will exercise
trustees is the comparative cost of delivering the same level of benefit over time
(assuming an inflationary impact on goods and wages), hence the preoccupa-
tion with the real returns on residual capital after current consumption. Tobin,
again, expresses this in the following terms:

They [the trustees] want to know, therefore, the rate of consumption from

endowment which can be sustained indefinitely. Sustainable consumption is

their conception of permanent endowment income.

Trustees in other circumstances may take a very different approach to dis-
tributing an endowment. Assume it is possible to eradicate a disease by
pumping money into a research program. The trustees will have a strong sub-
jective bias to present over future benefit and could justify disbursing the entire
endowment over a finite time to achieve their objective. As such, three types of
endowment can be distinguished:

● Infinitely lived — where rates of present consumption must not compromise future
sustainability.
● Finite certain — where the trustees have a fixed investment horizon and wish to
maximize returns through that time.
● Finite uncertain — where through unforeseen circumstances or the need to redirect
finances to an alternative objective, the maintenance of the residual real value of
capital can no longer be a priority.

3.7.4 The specification

Part 1 — Find the optimum drawdown by maximizing the expected utility function

UC C WTtTUC t BW T

t

T

(, ,, ) 01 (,) ( ,)

0

1

 





∑

where U ( C t , t ) is utility at time t depending on consumption at time t and
B ( W T , T ) is the bequest function (realized at the end of the charity’s existence),
which depends on the remaining wealth W T left as legacy.
If we consider infinitely lived charities, the utility function is:

UC C WTtUC t

t

(, ,, ) 01 (,)

0

 



∞

∑

The single period utility is defined as:

UC t UC

(,)δt ()