约束的Ross更加风险厌恶刻画下的预防性努力投资决策
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摘要
在对个体风险偏好的现有刻画下,一个更加风险厌恶的个体未必会投资更多的预防性努力活动.为了解决这种不一致性,本文基于二次函数约束的Ross更加风险厌恶的刻画,获得了与个体风险偏好相一致的比较静态结果:当额外的预防性努力活动降低了个体最终财富的均值且损失发生的初始概率小于1/2时,一个二次函数约束的Ross更加风险厌恶的个体总是投资更多的预防性努力活动.
A more risk averse individual does not always invest more in precautionary effort in the current characterization of individual risk preferences. This paper uses the characterization of quadratically-restricted Ross more risk aversion to resolve this inconsistency, and obtains some comparative static results consistent with individual's risk preferences: when additional precautionary effort always reduces the mean of final wealth, and the initial probability of loss is less than 1/2, a quadratically-restricted Ross more risk averse individual always invests more in precautionary effort.
A more risk averse individual does not always invest more in precautionary effort in the current characterization of individual risk preferences. This paper uses the characterization of quadratically-restricted Ross more risk aversion to resolve this inconsistency, and obtains some comparative static results consistent with individual's risk preferences: when additional precautionary effort always reduces the mean of final wealth, and the initial probability of loss is less than 1/2, a quadratically-restricted Ross more risk averse individual always invests more in precautionary effort.
引文
[1] Courbage C, Rey B, Treich N. Prevention and precaution. Handbook Insurance, 2nd Edition, New York:Springer, 2013:185-204
[2]田国强,田有功.不确定性下的高阶风险厌恶理论、实验及其应用.学术月刊,2017, 49(8):68-79(Tian G Q, Tian Y G. Theory, experimental evidences and applications of higher order risk aversion under uncertainty. Academic Monthly, 2017, 49(8):68-79)
[3] Ehrlich I, Becker G. Market insurance, self-insurance, and self-protection. J. Polit. Econ., 1972,80(4):623-648
[4] Lee K. Risk aversion and self-insurance-cum-protection. J. Risk Uncertain., 1998, 17(2):139-151
[5] Jindapon P, Neilson W. Higher-order generalizations of Arrow-Pratt and Ross risk aversion:a comparative statics approach. J. Econom. Theory, 2007, 136(1):719-728
[6] Eeckhoudt L, Huang R, Tzeng L. Precautionary effort:a new look. J. Risk Insurance, 2012, 79(2):585-590
[7] Wang J, Li J. Precautionary effort:another trait for prudence. J. Risk Insurance, 2015, 82(4):977-983
[8] Nocetti D. Robust comparative statics of risk changes. Manage. Sci., 2016, 62(5):1381-1392
[9] Arrow K. Aspects of the theory of risk bearing. Helsinki:Yrjo Jahnsson Foundation, 1965
[10] Pratt J. Risk aversion in the small and in the large. Econometrica, 1964, 32(12):122-136
[11] Ross S. Some stronger measures of risk aversion in the small and the large with applications. Econometrica, 1981, 49(3):621-638
[12] Eeckhoudt L, Gollier C. The impact of prudence on optimal prevention. Econom. Lett., 2005, 26(4):989-994
[13] Briys E, Schlesinger H. Risk aversion and the propensities for self-Insurance and self-protection.Southern Econom. J., 1990, 57(2):458-467
[14] Menezes C, Geiss C, Tressler J. Increasing downside risk. Am. Econ. Rev., 1980, 70(5):921-932
[15] Kimball M. Precautionary saving in the small and in the large. Econometrica, 1990, 58(1):53-73
[16] Denuit M, Eeckhoudt L, Liu L, Meyer J. Tradeoffs for downside risk-averse decision-makers and the self-protection decision. Geneva Risk Insurance Rev., 2016, 41(1):19-47
[17] Jullien B, Salanie B, Salanie F. Should more risk-averse agents exert more effort? Geneva Papers Risk Insurance Theory, 1999, 24(1):19-28
[18] Chiu W. Degree of downside risk aversion and self-protection. Insurance:Math. Econom., 2005,36(1):93-101
[19] Liu L, Rettenmaier A J, Saving T R. Conditional payments and self-protection. J. Risk Uncertain.,2009, 38(2):159-172
[20] Dionne G, Eeckhoudt L. Self-Insurance, self-protection and increased risk aversion. Econom. Lett.,1985, 17(1):39-42
[21] Eeckhoudt L, Liu L, Meyer J. Restricted increases in risk aversion and their application. Econom.Theory, 2017, 64(1):161-181
[22] Harsanyi J. Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. J. Polit.Econ., 1955, 63(4):309-321
[2]田国强,田有功.不确定性下的高阶风险厌恶理论、实验及其应用.学术月刊,2017, 49(8):68-79(Tian G Q, Tian Y G. Theory, experimental evidences and applications of higher order risk aversion under uncertainty. Academic Monthly, 2017, 49(8):68-79)
[3] Ehrlich I, Becker G. Market insurance, self-insurance, and self-protection. J. Polit. Econ., 1972,80(4):623-648
[4] Lee K. Risk aversion and self-insurance-cum-protection. J. Risk Uncertain., 1998, 17(2):139-151
[5] Jindapon P, Neilson W. Higher-order generalizations of Arrow-Pratt and Ross risk aversion:a comparative statics approach. J. Econom. Theory, 2007, 136(1):719-728
[6] Eeckhoudt L, Huang R, Tzeng L. Precautionary effort:a new look. J. Risk Insurance, 2012, 79(2):585-590
[7] Wang J, Li J. Precautionary effort:another trait for prudence. J. Risk Insurance, 2015, 82(4):977-983
[8] Nocetti D. Robust comparative statics of risk changes. Manage. Sci., 2016, 62(5):1381-1392
[9] Arrow K. Aspects of the theory of risk bearing. Helsinki:Yrjo Jahnsson Foundation, 1965
[10] Pratt J. Risk aversion in the small and in the large. Econometrica, 1964, 32(12):122-136
[11] Ross S. Some stronger measures of risk aversion in the small and the large with applications. Econometrica, 1981, 49(3):621-638
[12] Eeckhoudt L, Gollier C. The impact of prudence on optimal prevention. Econom. Lett., 2005, 26(4):989-994
[13] Briys E, Schlesinger H. Risk aversion and the propensities for self-Insurance and self-protection.Southern Econom. J., 1990, 57(2):458-467
[14] Menezes C, Geiss C, Tressler J. Increasing downside risk. Am. Econ. Rev., 1980, 70(5):921-932
[15] Kimball M. Precautionary saving in the small and in the large. Econometrica, 1990, 58(1):53-73
[16] Denuit M, Eeckhoudt L, Liu L, Meyer J. Tradeoffs for downside risk-averse decision-makers and the self-protection decision. Geneva Risk Insurance Rev., 2016, 41(1):19-47
[17] Jullien B, Salanie B, Salanie F. Should more risk-averse agents exert more effort? Geneva Papers Risk Insurance Theory, 1999, 24(1):19-28
[18] Chiu W. Degree of downside risk aversion and self-protection. Insurance:Math. Econom., 2005,36(1):93-101
[19] Liu L, Rettenmaier A J, Saving T R. Conditional payments and self-protection. J. Risk Uncertain.,2009, 38(2):159-172
[20] Dionne G, Eeckhoudt L. Self-Insurance, self-protection and increased risk aversion. Econom. Lett.,1985, 17(1):39-42
[21] Eeckhoudt L, Liu L, Meyer J. Restricted increases in risk aversion and their application. Econom.Theory, 2017, 64(1):161-181
[22] Harsanyi J. Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. J. Polit.Econ., 1955, 63(4):309-321