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

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2.3 Hidden Information or Full Information: the Sea Loan or the Commenda Standard contract theory informs us that in a one-period model contracts can only be made contingent on states whose occurrence can be verified to the satisfaction of all contracting parties (Townsend, 1982). The commenda is thus ruled out under hidden information since incentive- compatibility c2(x) = c2(x) = c2(¯x) (7) leads to a fix-repayment transfer regardless of the venture’s commercial profit: τ(x) = τ(x) = τ(¯x). Hidden information also restricts the upper bound of the parameter U 2 U 2 ≤ py U2[k2 − k + y] + [px + p¯x] U2[k2 − k + x] < E{U2[k2 − k + s]}. (8) As the merchant can expropriate the non-verifiable component of the profit, c1(¯x) ≥ ¯x − x > 0, contracts with τ(x) > x are non enforceable and the maximum utility that the financier can achieve is given by the value of U 2 in (8). The choice between the sea loan or the commenda can be simply rationalized in terms of the information structure: under hidden information, the parties are constrained to exchange through fix-payment sea loans, with τ(x) = τ(¯x); under full information, the incentive-compatibility constraint (7) is relaxed, enabling financial contracting through better risk-sharing commenda contracts, with τ(x) < τ(¯x). Yet, an explanation for the optimality of the sea loan or the commenda and for their evolution towards marine insurance as an independent for of business needs to account for the fact that both the sea loan and the commenda entailed the investor to recoup all the capital retrieved from a marine loss (τ(y) = y), whereas a premium insurance contract entailed the merchant to a coverage payment for such a loss (τ(y) < 0 ≤ y). 2.4 Optimal risk-sharing with k1 = 0 under hidden information Let us first examine the case in which the merchant is initially endowed with zero wealth and has hidden information on the true commercial return, so that he is constrained to resort to the 10
financier for the entire capital requirements and cannot commit to pay any amount beyond the verifiable venture’s returns. The programming problem becomes Program 2: max {c2(y),c2(x)} E{U1[w(s) − c2(s)]} s.t. E{U2[c2(s)]} = U 2 (9) c2(y) ≤ w(y), c2(x) ≤ w(x), c2(s) ≥ 0, (10) where U 2, satisfying (5) and (8), defines each individually-rational optimal allocation and restric- tion (10) combines the feasibility constraints (3) and (4) with the information constraint (7). Under hidden information, there are two instead of three choice variables and hence the optimal consumption allocation can be represented in a two-dimensional Edgeworth Box, but with a trick: the merchant’s consumption has two different origins. Each point in figures 1 to 4 thus represents the two event-contingent consumption of the financier and the three state-contingent consumption of the merchant. The dimensions of the Edgeworth Box are given by the total resources of the economy in each state, w(s) = k2 − k + s. Yet, the merchant’s inability to commit to refrain from embezzling the non-verifiable component of the profit leads to c2(x) ≤ w(x) and accounts for the shaded noncontractible area. [Figure 1 around here] From figure 1 it is clear without further analysis that any feasible allocation that provides constant consumption to the financier, i.e. c2(y) = c2(x) ≤ w(y) = k2 − k + y, does not satisfy his ex-ante participation constraint— P C2 in figures 1 to 4. Since the merchant is short of resources to pay out any amount beyond the venture’s verifiable returns, the financier is constrained to bear liability for loss of at least a part of his capital: τ(y) ≤ y < k. Would he optimally assume as little marine risk as possible through a sea loan, with τ(y) = y, or would he provide more insurance to the merchant, for example, by setting a coverage payment τ(y) < 0
Page 1 and 2: 1 Introduction The Birth of Insuran
Page 3 and 4: of hostile people, and to the inves
Page 5 and 6: utility from second-date consumptio
Page 7 and 8: in his enterity. In return for some
Page 9: ci(s) ≥ 0 ∀i, ∀s (3) ci(s)
Page 13 and 14: power U 2. 10 It is worth to note,
Page 15 and 16: of budget constraints (k1 = 0). How
Page 17 and 18: project is highly costly and risky
Page 19 and 20: parties commit part of their wealth
Page 21 and 22: commenda) because the high risk and
Page 23 and 24: the agents’ ability to diversify,
Page 25 and 26: It is proved below that at a soluti
Page 27 and 28: Show that dc2(y) d(k2−k) = −
Page 29 and 30: Program 3 is concave so that Kuhn-T
Page 31 and 32: When the entrepreneur lacks the wea
Page 33 and 34: [10] González de Lara, Y. “The S
Page 35 and 36: FIGURE 1 (Hidden Information, k1 =
Page 37: c1(y) ✛ FIGURE 5 (k1 > k, Two-sid

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