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Purpose and Abstract

Optimal Reciprocal Insurance Contract for Loss Aversion Preference Hung-Hsi Huang 黃鴻禧 National Chiayi University Ching-Ping Wang 汪青萍 National Kaohsiung University of Applied Sciences. Purpose and Abstract.

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Purpose and Abstract

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  1. Optimal Reciprocal Insurance Contract for Loss Aversion PreferenceHung-Hsi Huang 黃鴻禧National Chiayi UniversityChing-Ping Wang汪青萍National Kaohsiung University of Applied Sciences

  2. Purpose and Abstract • The reciprocal insurance contract is defined by maximizing the weighted expected wealth utility of the insured and the insurer. • For fitting the gap of the optimal insurance field, this study develops the reciprocal optimal insurance under the four situations: • risk-averse insured versus risk-averse insurer • risk-averse insured versus loss-averse insurer • loss-averse insured versus risk-averse insurer • loss-averse insured versus loss-averse insurer. 國立嘉義大學財務金融系

  3. Motivation • Kahneman and Tversky (1979) states that investors are characterized by a loss-averse utility preference, in which individuals are much more sensitive to losses than to gains. • Wang and Huang (2012) and Sung et al. (2011) have investigated the optimal insurance contract for maximizing a risk-averse insured’s objective against a risk-neutral insurer. 國立嘉義大學財務金融系

  4. Loss Aversion Behavior Evidence • Benartzi and Thaler (1995) found that the equity premium is consistent with the loss aversion utility. • Hwang and Satchell (2010) demonstrated that investors in financial markets are more loss averse than assumed in the literature. • In addition to individual loss aversion, several scholars have drawn on loss aversion to explain executive behaviors or institution risk-taking behaviors. • Devers et al. (2007) • O’Connell and Teo (2009) 國立嘉義大學財務金融系

  5. Optimal Insurance Studies • Raviv (1979, AER) is the pioneer who uses the optimal control theory in deriving the optimal insurance contract. • Extension • Uninsurable asset: Gollier (1996, JRI) • VaR (value-at-risk) constraint: Wang et al. (2005, GRIR), Huang (2006, GRIR), Zhou and Wu (2009, GRIR) • Expected loss constraint: Zhou and Wu (2008, IME) • Loss limit: Zhou et al. (2010, IME) 國立嘉義大學財務金融系

  6. Optimal Insurance for Prospect Theory • Wang and Huang (2012) developed an optimal insurance for loss aversion insured. • The representative optimal insurance form is the truncated deductible insurance. • When losses exceed a critical level, the insured retains all losses and adopts a particular deductible otherwise. • Sung et al. (2011) studied the optimal insurance policy with convex probability distortions. • Under a fixed premium rate, the results showed that either an insurance layer or a stop-loss insurance is an optimal insurance policy. 國立嘉義大學財務金融系

  7. Reciprocal Reinsurance • Cai et al. (2013, JRI) designed the optimal reinsurance treaty f that maximize • the joint survival probability • and the joint profitable probability. 國立嘉義大學財務金融系

  8. Loss, Premium, Wealth, Utility • Loss X and Premium P • Insured’s and Insurer’s final wealth • Objective of the optimal reinsurance 國立嘉義大學財務金融系

  9. S-shaped Loss Aversion Utility • Insured’s loss aversion utility • Insurer’s loss aversion utility 國立嘉義大學財務金融系

  10. The Optimal Reciprocal Insurance Form • Optimal indemnity schedule for RAU-RAU • Optimal indemnity schedule for RAU-LAU • Optimal indemnity schedule for LAU-RAU • Optimal indemnity schedule for LAU-LAU RAU = Risk Aversion Utility LAU = Loss Aversion Utility 國立嘉義大學財務金融系

  11. Optimal indemnity schedule for RAU-RAU • By calculus of variations, the Hamiltonian 國立嘉義大學財務金融系

  12. Optimal indemnity schedule for RAU-RAU • Proposition 1 for RAU-RAU: 國立嘉義大學財務金融系

  13. Unconstrained and Constrained Optimal Insurance • Unconstrained optimal reinsurance • Optimal insurance 國立嘉義大學財務金融系

  14. Optimal indemnity schedule for RAU-LAU Panel A Panel B Panel C 國立嘉義大學財務金融系

  15. Optimal indemnity schedule for RAU-LAU Panel A 國立嘉義大學財務金融系

  16. Optimal indemnity schedule for RAU-LAU Panel B 國立嘉義大學財務金融系

  17. Optimal indemnity schedule for RAU-LAU Panel C 國立嘉義大學財務金融系

  18. Optimal indemnity schedule for RAU-LAU 國立嘉義大學財務金融系

  19. Optimal indemnity schedule for RAU-LAU 國立嘉義大學財務金融系

  20. Optimal indemnity schedule for RAU-LAU • Panel A. for large λβ 國立嘉義大學財務金融系

  21. Optimal indemnity schedule for RAU-LAU • Panel B. for small λβ 國立嘉義大學財務金融系

  22. Optimal indemnity schedule for LAU-RAU Panel A Panel B Panel C 國立嘉義大學財務金融系

  23. Optimal indemnity schedule for LAU-RAU • Panel A. for small λ/α 國立嘉義大學財務金融系

  24. Optimal indemnity schedule for LAU-RAU • Panel B. for large λ/α 國立嘉義大學財務金融系

  25. Optimal indemnity schedule for LAU-LAU 國立嘉義大學財務金融系

  26. Optimal indemnity schedule for LAU-LAU Panel A 國立嘉義大學財務金融系

  27. Optimal indemnity schedule for LAU-LAU Panel B 國立嘉義大學財務金融系

  28. Optimal indemnity schedule for LAU-LAU Panel C 國立嘉義大學財務金融系

  29. Optimal indemnity schedule for LAU-LAU • Panel A. for small λ • Panel B. for large λ 國立嘉義大學財務金融系

  30. Optimal indemnity schedule for LAU-LAU • Panel C. for small λ 國立嘉義大學財務金融系

  31. Optimal indemnity schedule for LAU-LAU • Panel D. for large λ 國立嘉義大學財務金融系

  32. Optimal Premium and Coverage Level • For step 1, Section 3 derives the optimal indemnity schedule being a function of premium P. • Subsequently, this section aims to determine the optimal premium and the coverage level. 國立嘉義大學財務金融系

  33. Conclusions and Further Works 國立嘉義大學財務金融系

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