Precautionary Effort Investment under Cross Risk Aversion
1, Jie MEI 2, Wen CHENG 3, Sijie ZOU 4
1. Department of Teacher Education, Maanshan Teacher's College, Ma'anshan 243041, China;
2. Class 6, Grade 1, No.1 Middle School Affiliated to Central China Normal University, Wuhan 430223, China;
3. Department of Risk Management, China Huarong Asset Management Co., Ltd, Beijing 100033, China;
4. Department of Finance, Shandong Branch, China Three Gorges New Energy Co., Ltd, Jinan 277000, China
This paper deals with the effort problem under multiple risks in bivariate utility setting. We identify preference conditions to insure positive or negative effect of a background variable uncertainty on effort in the presence of other risks. We allow for the simultaneous presence of wealth and background variable uncertainties. We investigate the joint effect of two-source uncertainties on effort when two risks are either small or positive quadrant dependent. Our work extends the previous model of effort to bivariate utility framework and presents new insights into the issue of optimal effort under uncertainty.
Key words： precautionary effort
decision-making under uncertainty
Supported by the College Excellent Young Talents Program of Anhui (gxyq2017243) and the College Natural Science Foundation of Anhui Provincial Education Department (KJ2017A851)
Corresponding Authors: Wen CHENG,E-mail:email@example.com
About author: Yuqing TAO,E-mail:firstname.lastname@example.org;Jie MEI,E-mail:email@example.com;Sijie ZOU,E-mail:firstname.lastname@example.org
Ehrlich I, Becker G S. Market insurance, self-insurance, and self-protection. Journal of Political Economy, 1972, 80:623-648.
Dionne G, Eeckhoudt, L. Self-insurance, self-protection and increased risk aversion. Economics Letters, 1985, 17:39-42.
Briys E, Schlesinger H. Risk aversion and the propensities for self-insurance and self-protection. Southern Economic Journal, 1990, 57:458-467.
Chiu W H. Degree of downside risk aversion and self-protection. Insurance:Mathematics and Economics, 2005, 36(1):93-101.
Eeckhoudt L, Gollier C. The impact of prudence on optimal prevention. Economic Theory, 2005, 26:989-994.
Menegatti M. Optimal prevention and prudence in a two-period model. Mathematical Social Sciences, 2009, 58:393-397.
Dionne G, Li J. The impact of prudence on optimal prevention revisited. Economics Letters, 2011, 113:147-149.
Tao Y, Cheng W, Zou S. Priority setting in health care with disease and treatment risks. Journal of Systems Science and Information, 2018, 6:552-562.
Brianti M, Magnani M, Menegatti M. Optimal choice of prevention and cure under uncertainty on disease effect and cure effectiveness. Research in Economics, 2018, 72:327-342.
Lee K. Background risk and self-protection. Economics Letters, 2012, 114:262-264.
Courbage C, Rey B. Optimal prevention and other risks in a two-period model. Mathematical Social Sciences, 2012, 63:213-217.
Jullien B, Salanie B, Salanie F. Should more risk averse agents exert more effort. Geneva Papers on Risk and Insurance Theory, 1999, 24:19-25.
Chuang O, Eeckhoudt L, Huang R J, et al. Risky targets and effort. Insurance:Mathematics and Economics, 2013, 52:465-468.
Jindapon P, Neilson W. Higher-order generalizations of Arrow-Pratt and Ross risk aversion:A comparative statics approach. Journal of Economic Theory, 2007, 136:719-728.
Courbage C, Rey B. Precautionary saving in the presence of other risks. Economic Theory, 2007, 32:417-424.
Menegatti M. Precautionary saving in the presence of two risks. Journal of Economics, 2009, 96:277-288.
Li J. Precautionary saving in the presence of labor income and interest rate risks. Journal of Economics, 2011, 106:251-266.
Denuit M M, Eeckhoudt L, Menegatti M. Correlated risks, bivariate utility and optimal choices. Economic Theory, 2011, 46:39-54.
Pratt J W. Aversion to one risk in the presence of others. Journal of Risk and Uncertainty, 1988, 1:395-413.
Finkelshtain I, Kella O, Scarsini M. On risk aversion with two risks. Journal of Mathematical Economics, 1999, 31:239-250.
Eeckhoudt L, Rey B, Schlesinger H. A good sign for multivariate risk taking. Management Science, 2007, 53:117-124.
Lehmann E L. Some concepts of dependence. Annals of Mathematical Statistics, 1966, 37:1137-1153.
Gollier C. The consumption-based determinants of the term structure of discount rates. Mathematics and Financial Economics, 2007, 1:81-102.
Rothschild M, Stiglitz J. Increasing risk I:A definition. Journal of Economic Theory, 1970, 2:55-243.
Kimball M S. Precautionary savings in the small and in the large. Econometrica, 1990, 58:53-73.
Courbage C, Rey B. On non-monetary measures in the face of risks and the signs of the derivatives. Bulletin of Economic Research, 2010, 62(3):0307-3378.
Chiu W H. Skewness preference, risk aversion, and the precedence relations on stochastic changes. Management Science, 2005, 51(12):1816-1828.
Denuit M M, Eeckhoudt L. A general index of absolute risk attitude. Management Science, 2010, 56(4):712-715.
Eeckhoudt L, Huang R J, Tzeng L Y. Precautionary effort:A new look. Journal of Risk and Insurance, 2012, 79:585-590.
Eeckhoudt L, Etner J, Schroyen F. The values of relative risk aversion and prudence:A context-free interpretation. Mathematical Social Sciences, 2009, 58:1-7.
Wang J, Li J. Multiplicative risk apportionment. Mathematical Social Sciences, 2010, 60:79-81.
Chiu W H, Eeckhoudt L, Rey B. On relative and partial risk attitudes:Theory and implications. Economic Theory, 2012, 50:151-167.
Denuit M, Rey B. Benchmark values for higher order coefficients of relative risk aversion. Theory and Decision, 2014, 76:81-94.