Can a Buddhist own and run a billion dollar business? China, Japan, Korea, etc. have so many companies and Buddhism is widespread in those areas. My question is: can a Buddhist make the aim of his life to run a billion dollar business?
Sure! It is allowed for lay people, as long as they observe the five precepts and virtue (sila), which includes Right Livelihood (samma ajivo). Please also see this answer.
The Vanijja Sutta states:

&quot;Monks, a lay follower should not engage in five types of business.
Which five? Business in weapons, business in human beings, business in
meat, business in intoxicants, and business in poison.
&quot;These are the five types of business that a lay follower should not
engage in.&quot;

The Sigalovada Sutta states:

The wise endowed with virtue
Shine forth like a burning fire,
Gathering wealth as bees do honey
And heaping it up like an ant hill.
Once wealth is accumulated,
Family and household life may follow.
By dividing wealth into four parts,
True friendships are bound;
One part should be enjoyed;
Two parts invested in business;
And the fourth set aside
Against future misfortunes.&quot;

The Dighajanu Sutta states:

&quot;And what does it mean to maintain one's livelihood in tune? There is
the case where a lay person, knowing the income and outflow of his
wealth, maintains a livelihood in tune, neither a spendthrift nor a
penny-pincher, [thinking], 'Thus will my income exceed my outflow, and
my outflow will not exceed my income.'

The Adiya Sutta talks about the five types of benefits that can be obtained from wealth, which are summarized below:

'My wealth has been enjoyed,
my dependents supported,
protected from calamities by me.
I have given supreme offerings
&amp; performed the five oblations.
I have provided for the virtuous,
the restrained,
followers of the holy life.
For whatever aim a wise householder
would desire wealth,
that aim I have attained.
I have done what will not lead to future distress.'
When this is recollected by a mortal,
a person established in the Dhamma of the Noble Ones,
he is praised in this life
and, after death, rejoices in heaven.

Also from the Anana Sutta which talks about &quot;the four kinds of bliss that can be attained in the proper season, on the proper occasions, by a householder partaking of sensuality&quot;, summarizes it as follows:

Knowing the bliss of debtlessness,
&amp; recollecting the bliss of having,
enjoying the bliss of wealth,
the mortal then sees clearly with discernment.
Seeing clearly — the wise one —
he knows both sides:
that these are not worth one sixteenth-sixteenth
of the bliss of blamelessness.

Billionaire businessmen can support society by creating jobs, fulfill the needs and wants of the people through supply for demand, and be philanthropists (similar to Bill Gates and Warren Buffett) who donate to charitable causes and also to Buddhist causes.
As pointed out by Samana Johann, Anathapindika is a great example of a very wealthy man in the time of the Buddha, who used his wealth to contribute to the spread of the Dhamma.

Anathapindika had many carts filled with gold coins, and had them
spread out upon the site. Finally only one small patch of ground at
the entrance remained bare. He gave the instructions that more gold be
brought, but the Prince Jeta announced that he was prepared to build a
mighty gate-tower on that spot at his own expense. This imposing
bastion and gate protected the monastery from the outside world,
shielded it from the noises of the road, and emphasized the dividing
line between the realms of the sacred and the worldly. Anathapindika
then spent another eighteen million for buildings and furnishings. He
built individual cells, a meeting hall, a dining hall, storerooms,
walkways, latrines, wells, and lotus ponds for bathing as well as a
large surrounding wall. Thus the forest glade was transformed into a
monastery and stood apart as a religious sanctuary.


Addendum:
Added later to show the benefit of using one's wealth to give gifts to &quot;the upright ones&quot;.
This is the story of householder Ugga of Vesālī, who gave a lot of gifts to the Buddha. The Buddha accepted them out of compassion. I only quote the final portion of the sutta here.
From the Manāpadāyī Sutta:

“Bhante, in the presence of the Blessed One I heard and learned this:
‘The giver of what is agreeable gains what is agreeable.’ Bhante, my
couch spread with rugs, blankets, and covers, with an excellent
covering of antelope hide, with a canopy above and red bolsters at
both ends, is agreeable. Although I know this is not allowable for the
Blessed One, this sandalwood plank of mine is worth over a thousand.
Let the Blessed One accept it from me, out of compassion.” The Blessed
One accepted, out of compassion.
Then the Blessed One expressed his appreciation to the householder
Ugga of Vesālī thus:

“The giver of the agreeable gains the agreeable,
when he gives willingly to the upright ones
clothing, bedding, food, and drink,
and various kinds of requisites.
“Having known the arahants to be like a field
for what is relinquished and offered, not held back,
the good person gives what is hard to give:
the giver of agreeable things gains what is agreeable.”

Then, after expressing his appreciation to the householder Ugga of
Vesālī, the Blessed One rose from his seat and left. Then, some time
later, the householder Ugga of Vesālī passed away. After his death,
the householder Ugga of Vesālī was reborn among a certain group of
mind-made deities. On that occasion the Blessed One was dwelling at
Sāvatthī in Jeta’s Grove, Anāthapiṇḍika’s Park. Then, when the night
had advanced, the young deva Ugga, of stunning beauty, illuminating
the entire Jeta’s Grove, approached the Blessed One, paid homage to
him, and stood to one side. The Blessed One then said to him: “I hope,
Ugga, that it is as you would have wished.”
“Surely, Bhante, it is as I had wished.”
Then the Blessed One addressed the young deva Ugga with verses:

“The giver of the agreeable gains the agreeable;
the giver of the foremost again gains the foremost;
the giver of the excellent gains the excellent;
the giver of the best reaches the best state.
“The person who gives the best,
the giver of the foremost,
the giver of the excellent,
is long-lived and famous
wherever he is reborn.”