Correlated risks, bivariate utility and optimal choices

In this paper, we consider a decision-maker facing a financial risk flanked by a non-financial background risk such as health or environmental risk. A decision has to be made about the amount of an investment (in the financial dimension) resulting in a future benefit either in the same dimension (savings) or in the other dimension (environmental quality or health improvement). In this framework, we study the impact of the correlation between the two risks on optimal choices. In the saving problem, we find conditions ensuring that positive correlation between the two risks implies that the optimal amount of savings increases. These conditions involve specific requirements on the direct and cross derivatives of the two-argument utility function. Similarly, we find a different and specific set of conditions ensuring that the same conclusion on optimal investment for health (environmental) improvement is reached. The two sets of conditions determined support the conclusion that the signs of the derivatives of the two-argument utility function should alternate.

[1]  Miles S. Kimball.  Precautionary Saving in the Small and in the Large , 1989 .

[2]  Andreas Wagener,et al.  Variance Vulnerability, Background Risks, and Mean-Variance Preferences , 2003 .

[3]  Christian M. Hafner,et al.  Estimating Autocorrelations in the Presence of Deterministic Trends , 2011 .

[4]  Andreas Wagener,et al.  Multiple Risks and Mean-Variance Preferences , 2009, Oper. Res..

[5]  Louis Eeckhoudt,et al.  Background Risk, Prudence, and the Demand for Insurance , 1992 .

[6]  J. Krawczyk,et al.  Towards an understanding of tradeoffs between regional wealth, tightness of a common environmental constraint and the sharing rules , 2010 .

[7]  Mario Menegatti.  Optimal saving in the presence of two risks , 2009 .

[8]  V. Ginsburgh,et al.  Handbook of the Economics of the Art and Culture , 2006 .

[9]  Carlo Rosa,et al.  Forecasting the Direction of Policy Rate Changes: The Importance of ECB Words , 2009 .

[10]  Precautionary saving in the presence of other risks , 2007 .

[11]  Christian Gourieroux,et al.  Simulation-based econometric methods , 1996 .

[12]  Collin Carbno,et al.  Actuarial Theory for Dependent Risks: Measures, Orders, and Models , 2007, Technometrics.

[13]  Jacques-François Thisse,et al.  Economic Geography: The Integration of Regions and Nations , 2008 .

[14]  Agnar Sandmo,et al.  The Effect of Uncertainty on Saving Decisions , 1970 .

[15]  R. Luttens,et al.  Voting for Redistribution Under Desert‐Sensitive Altruism , 2012 .

[16]  A. Atkinson,et al.  The Comparison of Multi-Dimensioned Distributions of Economic Status , 1982 .

[17]  S. Ekern.  Increasing Nth degree risk , 1980 .

[18]  Mario Menegatti,et al.  On the Conditions for Precautionary Saving , 2001, J. Econ. Theory.

[19]  Louis Eeckhoudt,et al.  Changes in Background Risk and Risk Taking Behavior , 1996 .

[20]  Mario Menegatti.  Precautionary saving in the presence of other risks: a comment , 2009 .

[21]  M. Denuit,et al.  A class of bivariate stochastic orderings, with applications in actuarial sciences , 1999 .

[22]  John W. Pratt,et al.  Aversion to one risk in the presence of others , 1988 .

[23]  W. Sharpe.  Portfolio Theory and Capital Markets , 1970 .

[24]  Daniel Bienstock,et al.  Potential Function Methods for Approximately Solving Linear Programming Problems: Theory and Practice , 2002 .

[25]  Larry G. Epstein,et al.  Increasing Generalized Correlation: A Definition and Some Economic Consequences , 1980 .

[26]  Jean-François Mertens,et al.  Regularity and stability of equilibria in an overlapping generations model with exogenous growth , 2009 .

[27]  Henry Tulkens,et al.  The impact of the unilateral EU commitment on the stability of international climate agreements , 2010 .

[28]  Nicolas Gillis,et al.  Using underapproximations for sparse nonnegative matrix factorization , 2009, Pattern Recognit..

[29]  Robert L. Winkler,et al.  Risky Choices and Correlated Background Risk , 2005, Manag. Sci..

[30]  M. Scarsini,et al.  On risk aversion with two risks , 1999 .

[31]  Leonard J. Mirman,et al.  Risk aversion with many commodities , 1974 .

[32]  Jean Jaskold Gabszewicz,et al.  Public goods’ attractiveness and migrations , 2008 .

[33]  Michel Denuit,et al.  Bivariate stochastic dominance and common preferences of decision-makers with risk independent utilities , 2010 .

[34]  James Renegar,et al.  A mathematical view of interior-point methods in convex optimization , 2001, MPS-SIAM series on optimization.

[35]  Harris Schlesinger,et al.  Optimal Insurance in Incomplete Markets , 1983, Journal of Political Economy.

[36]  J. Dávila,et al.  The taxation of capital returns in overlapping generations economies without Financial assets , 2008 .

[37]  Laurence A. Wolsey,et al.  Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 4th International Conference, CPAIOR 2007, Brussels, Belgium, May 23-26, 2007, Proceedings , 2007, CPAIOR.

[38]  Santanu S. Dey.  A note on the split rank of intersection cuts , 2011, Math. Program..

[39]  H. Leland..  Saving and Uncertainty: The Precautionary Demand for Saving , 1968 .

[40]  Çagatay Kayi,et al.  Characterizations of Pareto-efficient, fair, and strategy-proof allocation rules in queueing problems , 2010, Games Econ. Behav..

[41]  Louis Eeckhoudt,et al.  Changes in Risk and the Demand for Saving , 2008, SSRN Electronic Journal.

[42]  Louis Eeckhoudt,et al.  A Good Sign for Multivariate Risk Taking , 2006, Manag. Sci..

[43]  J. Rombouts,et al.  Style Rotation and Performance Persistence of Mutual Funds , 2009 .

[44]  Michel Denuit,et al.  Extremal generators and extremal distributions for the continuous s-convex stochastic orderings , 1999 .

[45]  Michel Denuit,et al.  Some consequences of correlation aversion in decision science , 2010, Ann. Oper. Res..

[46]  Miles S. Kimball,et al.  Standard Risk Aversion , 1991 .

[47]  Moshe Shaked,et al.  The s-convex orders among real random variables, with applications , 1998 .

[48]  Jacek B. Krawczyk,et al.  A viability theory approach to a two-stage optimal control problem of technology adoption , 2007 .