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

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FIGURE 4 (Hidden In<strong>for</strong>mation, k1 = 0, Two-side Risk Aversion, c2(x) Higly Costly and Risky Venture) ✻ ✛ ✛ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ✲ ❄ A ❆ ❆ ❚ ❚ ❚ ❏❏ ❏ ❏ ❏ ❏ ❭ ❭ ❭ ❧ ❧ ❧ ❩ ❩ ❩P C2 ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ CCλk1 =0 ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡✡ ✡ ✡✡ ✡ ✡✡ ✡ ✡✡ ✡ ✡ ✡ ✡ ✡✡ ✡ ✡✡✡ ✡ ✡✡ ✡ ✡✡ Agent 1(the merchant) (0,0) if x =¯x c1(y) (0,0) if x =x c1(y) c2(y) Agent 2 (0,0) k2 − k + y (the financier) c1(x) k2 − k + t k2 cc k2 − k + t pc k2 − k + x sea loan: τ = − k τ(y) = y τ(x) = τ(¯x) = τ(x) = ˜t ≥ t pc //////////////////////// //////////////////////// //////////////////////// //////////////////////// Noncontractible area //////////////////////// //////////////////////// //////////////////////// //////////////////////// //////////////////////// ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ✉ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 36
c1(y) ✛ FIGURE 5 (k1 > k, Two-side Risk Aversion, Higly Costly and Risky Venture) k2 − k + x c2(x) Agent 2 (0,0) (the financier) ✻ k1 k1 − k + y . . . . . . . . . . . . . . . . . . . BP2 . ✓ ✓✓ ✓ ✓✓ ✓ ✓✓ ✓ ✓✓ ✓ ✓✓✓✓ CCλk1 >k ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓✓ ✓ ✓ ✓ ✓ ✓ ❝❝ ❧ ❧ ❅ ❅ ❅ ❙ ❙ ❙❙ ❙ ❚ ❙ Ex-ante P C1 ❚ ❙ ❏ ❧ ❏ ❧ ❏ ❧ ❝ ❏ ❝ ❆ ❝ . . . . . . . . . . . . k1 . BP1 . . k2 . . . . . . . . . . . . A. . . . . . . k1 − k + x . ✡ . ✡✡ ✡ ✡✡ CCλk1 =0 ✡ ✡ ✡ ✡ ✡✡ ✡ ✡✡ ✡ ✡✡ ✓ ✓✓ ✓ ✓✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ❩ ❆ ❩❩◗◗◗❍❍Ex-ante ✓ ❆ Individual Rationality ❆ (k1 > k) ❆ ❇ P C2 ≡ ❇❇ Individual Rationality ✡ ✡✡ ✡ ✡✡✡ ✡ ✡✡ ✓ ✓✓✓ ✓ ✓✓✓ ✓ ✓✓✓ ✓ ✓✓✓ ✓ ✓✓✓ ✡ ✡✡ ✡ ✡ ✡ ✡✡ ✓ ✓✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ . . . . . . . . . . . . . . . (0,0) . ✲ ❄ ❄ k2 − k + y k2 k1 + k2 − k + y k2 − k + y < c ∗ 2(y) = k2 − k + y + ɛ < k2 37 Agent 1 (the merchant) c2(y)
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 and 10: ci(s) ≥ 0 ∀i, ∀s (3) ci(s)
Page 11 and 12: financier for the entire capital re
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: FIGURE 1 (Hidden Information, k1 =

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