The Birth of Insurance Contracts - The Ataturk Institute for Modern ...

Proposition 1 The more risky and costly the venture is (the higher py and the lower y, the higher
k relative to k2, and the lower E[x] = px x + p¯x ¯x given x ≥ t pc ), the more likely it is that the risk
averse merchant raises funds from the risk averse financier through a sea loan, optimally.
If the venture is highly risky and costly, the financier might suffer a substantial loss. On the
likely event of a navigation incident (py high), he cannot recoup any amount beyond what is saved
from misfortune, which is dreadfully insufficient (y very low) to reward his capital investment:
τ(y) ≤ y ≪ k. This implies a very significant loss to him, for he has invested a major part of
his scarce initial endowment in the costly venture (k high relative to k2). To compensate for the
possibility of loss, the financier requires soaring payments when the merchandise arrived at port
safe and sound. As a consequence, his consumption varies widely, whereas that of the merchant
is invariably small. At any feasible and individually-rational allocation,
c2(y) ≤ k2 − k + y, c2(x) ≥ k2 − k + ˜t, and c1(y) ≥ 0, E[c1(x)] ≤ E[x] − ˜t,
where ˜t ∈ [t pc , x] denotes the transfer required by the investor to compensate him for assuming as
less marine risk as possible, i.e. the very high transfer a sea loan establishes on the event of safe
arrival of the ship and its cargo to destination. The second and fourth inequalities derive from
the downward slope of the financier’s indifference curves (see figure 1 and 4). Thus, on the choice
set the merchant’s consumption is smoother than the financier’s consumption
max{E[c1(x)] − c1(y)} = E[x] − ˜t ≪ ˜t − y = min{c2(x) − c2(y)}. (11)
Because both agents are assumed to have the same preferences, the merchant values insurance
relatively less than the financier so that it is optimal that he receives as less marine insurance as
possible. Since the higher the amount paid out in the case of loss, the lower the repayment required
otherwise and the less volatile the investor’s event-consumption relative to the merchant’s, it is
optimal that the investor recoup as much of his capital as possible from the venture’s return. A
sea loan, establishing τ = −k, τ(y) = y, and τ(x) = τ(¯x) = ˜t, can sustain all the allocations in
the core, with ˜t ∈ [t pc , x] taking different values for each individually-rational level of bargaining
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