Lecture Notes for Finance 1 (and More).

Chapter 3
Payment Streams under
Certainty
3.1 Financial markets and arbitrage
In this section we consider a very simple setup with no uncertainty. There
are three reasons that we do this:
First, the terminology of bond markets is conveniently introduced in this
setting, for even if there were uncertainty in our model, bonds would be
characterized by having payments whose size at any date are constant and
known in advance.
Second, the classical net present value (NPV) rule of capital budgeting is
easily understood in this framework.
And finally, the mathematics introduced in this section will be extremely
useful in later chapters as well.
A note on notation: If v ∈ R N is a vector the following conventions for
“vector positivity” are used:
• v ≥ 0 (“v is non-negative”) means that all of v ′ s coordinates are nonnegative.
ie. ∀i: vi ≥ 0.
• v > 0 (“v is positive” ) means that v ≥ 0 and that at least one coordinate
is strictly positive, ie. ∀i: vi ≥ 0 and ∃i: vi > 0, or differently
that v ≥ 0 and v �= 0.
• v ≫ 0 (“v is strictly positive”) means that every coordinate is strictly
positive, ∀i: vi > 0. This (when v is N-dimensional) we will sometimes
write as v ∈ RN ++ . (This saves a bit of space, when we want to indicate
both strict positivity and the dimension of v.)
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net present value,
NPV
positivity of
vectors