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Risk Transfer Efficiency

Exposition Title. Risk Transfer Efficiency. Presented by SAIDI Neji University Tunis El-Manar. Problematical. What are impacts of attitudes toward risk on transfer possibilities  ?;. How can we characterize added value and Pareto Optimum allocations?;.

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Risk Transfer Efficiency

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  1. Exposition Title Risk Transfer Efficiency Presented by SAIDI Neji University Tunis El-Manar

  2. Problematical • What are impacts of attitudes toward risk on transfer possibilities  ?; • How can we characterize added value and Pareto Optimum allocations?; • What tie can we establish between added value maximization and optimum de Pareto within RDEU model?. 

  3. Introduction: Uncertainty Typology • Typology from source ( Nature or adversaries) • Typology from information degree: If we have de probability distribution P over (S=Ω,Γ), we have risk situation, else we are in uncertainty. • A lottery is noted X=(x1,p1 ;… ; xn, pn) • On assimilate a decision to risky variable

  4. a. Expected Utility Model ch 1:Risk decisions 1. Risk decision models b.Mean-variancemodel

  5. 2. Attitudes toward risk • Risk Aversion :vN-M function is concave • Risk lover : vN-M function is convex. • Risk neutrality: vN-M function is linear Pratt(1964) and Arrow (1965) proposed risk aversion measures in order to compare individual behaviors. They conclude that some agents are more able to bear risk

  6. 3. Risk transfer examples • a/ Insurance • Mossin (1968), optimal contract is: • Full coverage if premium is equitable • Co-assurance (agent preserve a lottery portion)if premium is loaded b/Ask for risky assets (investment): diversification

  7. 4. EUModel weaknesses • Allais (1953); Kahenman et Tversky (1979) starting point of rank dependant expected utility model (RDEU) • For X=(xi,pi)i=1,…,n where x1 <….<xn , we have : • Particular case: dual theory (Yaari (1987))

  8. Tableau 1:Behavior Characterizations in risk

  9. Partie 2: Risk Transfer Efficiency 1. Theoretical antecedents • Risk sharing (P.O) in EU setting: Borch(1962), Arrow(1971), Raiffa(1970), Eeckhoudt and Gollier(1992). • Eeckhoudt and Roger (1994,1998): added value

  10. 2. Analyze framework and definitions a/Hypothesis • Our analysis is restricted to two economic agents • The first has a composed wealth of a certain part W1 and of a lottery X • the initial wealth W2 of the second agent is certain • Every agent i (i=1,2) characterizes himself by a relation of preferences on the set of lotteries noted. • X admits an equivalent certain unique EC(X)

  11. b/Definitions • Selling Price pV (W1,αX) defined by: • Buying Price pA (W1,αX) defined by: • If transfer occurs, then the difference: s(α)= pa (W2, α X) - pv (W1, α X) is called transfer added value (or social surplus).

  12. 3.Main results 3.1. Transfer possibilities Proposition 1 a/ If E(X) ≤0 and DARA agents with W1≤W2, then transfer occurs b/ If first agent is risk averse and second one is neutral, then proportional transfer is realizable. c/ Within Yaari model, risk transfer is possible if and only if  : DT1(X) ≤ DT2(X)

  13. Condition: DT1(X) ≤ DT2(X), can be interpreted as first agent is more pessimist than second one 3.2. Added value maximization Proposition 2 We have Max s(α ) by a total transfer (α* =1) if: a/ First agent is risk averse and second one is neutral b/ Within Yaari model with DT1(X) ≤ DT2(X)

  14. 3.3. Relation between social welfare et Pareto optimum Social utility function with Proposition 3 1. An allocation maximizing F is Pareto efficient 2. If Utility possibilities set of two agents is convex, then an allocation is Pareto optimal if and only if it maximize F

  15. Proposition 4 If agents were risk averse in RDEU model, with concaves and differentials utility functions, then an allocation (W1,W2) is Pareto optimal if and only if it maximize F If agents have the same probabilities transformation function, then:

  16. Proposition 5 In Yaari model, Pareto optimal allocations were realized by assets total transfer and respond to following conditions  : i/ If λ>1 then price is DT1(X) ; ii/ If λ=1 then price  [DT1(X), DT2(X)] ; iii/ If λ<1 then price is DT1(X) DT2(X).

  17. Figure 1. Optimal Pareto Allocations O2 w21 O1 w11 optimum in EU model optimum in Yaari model

  18. Tableau 2: Relations between welfare and added value

  19. 1st application: optimal loading within dual theory (E(X)<0)

  20. 2eme application : Transfer by intermediate An intermediate who seek to guarantee a spread αЛ0 by transferring a portion αX The surplus will be divided between agent 2 et intermediate The surplus will be divided between three agents. The surplus will be divided between buyer et intermediate

  21. Intermediate provide new complication to transfer study. In fact, in addition to agents preferences, exchange possibility will be affected by market maker behavior. Thus, fixed spread by intermediate depend: • intermediate preferences • His inventory (stock effect) • His information's (pessimism degree)

  22. Thank You for care

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