American Institute of Mathematical Sciences

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January  2011, 7(1): 139-156. doi: 10.3934/jimo.2011.7.139

Optimal consumption and investment under irrational beliefs

Lei Sun 1, and  Lihong Zhang 2,

1. 

School of Business and Management, Hong Kong University of Science and Technology, Hong Kong, China
2. 

School of Economics and Management, Tsinghua University, Beijing, China

Received  March 2010 Revised  October 2010 Published  January 2011

In this paper, we study how irrationality affects the investor's consumption and investment decisions. We build a continuous-time financial model, where an irrational investor determines his consumption and investment according to an exogenous price process. The main results are as follows. First, compared with a rational investor, an optimistic irrational investor tends to consume more, while a pessimistic irrational investor tends to consume less. Second, the more irrational the investor, the more volatile his consumption. Third, the extremely irrational investor can get more ex ante expected utility than his rational counterpart, no matter he is optimistic or pessimistic.
Keywords: consumption., optimization, Irrational belief, investment.
Mathematics Subject Classification: Primary: 91B28; Secondary: 91B08, 91B16, 91B7.
Citation: Lei Sun, Lihong Zhang. Optimal consumption and investment under irrational beliefs. Journal of Industrial & Management Optimization, 2011, 7 (1) : 139-156. doi: 10.3934/jimo.2011.7.139
References:
[1]

Armen A. Alchian, Uncertainty, evolution, and economic theory, Journal of Political Economy, 58 (1950), 211-221. doi: 10.1086/256940.  Google Scholar

[2]

Fisher Black, Noise, Journal of Finance, 41 (1986), 529-543. doi: 10.2307/2328481.  Google Scholar

[3]

Fisher Black and Myron Scholes, The valuation of options and corporate liabilities, Journal of Political Economy, 81 (1973), 637-654. doi: 10.1086/260062.  Google Scholar

[4]

Lawrence Blume and David Easley, If you are so smart, why aren't you rich? Belief selection in complete and incomplete markets, Econometrica, 74 (2006), 929-966. doi: 10.1111/j.1468-0262.2006.00691.x.  Google Scholar

[5]

J. Bradford De Long, Andrei Shleifer, Lawrence H. Summers and Robert J. Waldman, The survival of noise traders in financial markets, Journal of Business, 64 (1991), 1-19. Google Scholar

[6]

Yuri Fedyk and Johan Walden, High-speed natural selection in financial markets with large state spaces, Working paper, Hass School of Business, UC Berkeley, 2007. Google Scholar

[7]

Milton Friedman, "Essays in Positive Economics," University of Chicago Press, Chicago, 1953. Google Scholar

[8]

Lars P. Hansen and Scott Richard, The role of conditioning information in deducing testable restrictions implied by dynamic asset pricing models, Econometrica, 55 (1987), 587-613. doi: 10.2307/1913601.  Google Scholar

[9]

John M. Harrison and David M. Kreps, Martingales and arbitrage in multiperiod securities markets, Journal of Economic Theory, 20 (1979), 381-408. doi: 10.1016/0022-0531(79)90043-7.  Google Scholar

[10]

David Hirshleifer, Avanidhar Subrahmanyam and Sheridan Titman, Feedback and the success of irrational investors, Journal of Financial Economics, 81 (2006), 311-338. doi: 10.1016/j.jfineco.2005.05.006.  Google Scholar

[11]

Ioannis Karatzas and Steven E. Shreve, "Methods of Mathematical Finance," Springer-Verlag, New York, 1998.  Google Scholar

[12]

Leonid Kogan, Stephen A. Ross, Jiang Wang and Mark M. Westerfield, The price impact and survival of irrational traders, Journal of Finance, 61 (2006), 195-229. doi: 10.1111/j.1540-6261.2006.00834.x.  Google Scholar

[13]

John Lintner, The valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics, 47 (1965), 13-37. doi: 10.2307/1924119.  Google Scholar

[14]

Robert C. Merton, An intertemporal capital asset pricing model, Econometrica, 41 (1973), 867-887. doi: 10.2307/1913811.  Google Scholar

[15]

Stephen A. Ross, The arbitrage theory of capital asset pricing, Journal of Economic Theory, 13 (1976), 341-360. doi: 10.1016/0022-0531(76)90046-6.  Google Scholar

[16]

Alvaro Sandroni, Do markets favor agents able to make accurate predictions?, Econometrica, 68 (2000), 1303-1341. doi: 10.1111/1468-0262.00163.  Google Scholar

[17]

William Sharpe, Capital asset prices: a theory of market equilibrium under conditions of risk, Journal of Finance, 19 (1964), 425-442. doi: 10.2307/2977928.  Google Scholar

show all references

References:
[1]

Armen A. Alchian, Uncertainty, evolution, and economic theory, Journal of Political Economy, 58 (1950), 211-221. doi: 10.1086/256940.  Google Scholar

[2]

Fisher Black, Noise, Journal of Finance, 41 (1986), 529-543. doi: 10.2307/2328481.  Google Scholar

[3]

Fisher Black and Myron Scholes, The valuation of options and corporate liabilities, Journal of Political Economy, 81 (1973), 637-654. doi: 10.1086/260062.  Google Scholar

[4]

Lawrence Blume and David Easley, If you are so smart, why aren't you rich? Belief selection in complete and incomplete markets, Econometrica, 74 (2006), 929-966. doi: 10.1111/j.1468-0262.2006.00691.x.  Google Scholar

[5]

J. Bradford De Long, Andrei Shleifer, Lawrence H. Summers and Robert J. Waldman, The survival of noise traders in financial markets, Journal of Business, 64 (1991), 1-19. Google Scholar

[6]

Yuri Fedyk and Johan Walden, High-speed natural selection in financial markets with large state spaces, Working paper, Hass School of Business, UC Berkeley, 2007. Google Scholar

[7]

Milton Friedman, "Essays in Positive Economics," University of Chicago Press, Chicago, 1953. Google Scholar

[8]

Lars P. Hansen and Scott Richard, The role of conditioning information in deducing testable restrictions implied by dynamic asset pricing models, Econometrica, 55 (1987), 587-613. doi: 10.2307/1913601.  Google Scholar

[9]

John M. Harrison and David M. Kreps, Martingales and arbitrage in multiperiod securities markets, Journal of Economic Theory, 20 (1979), 381-408. doi: 10.1016/0022-0531(79)90043-7.  Google Scholar

[10]

David Hirshleifer, Avanidhar Subrahmanyam and Sheridan Titman, Feedback and the success of irrational investors, Journal of Financial Economics, 81 (2006), 311-338. doi: 10.1016/j.jfineco.2005.05.006.  Google Scholar

[11]

Ioannis Karatzas and Steven E. Shreve, "Methods of Mathematical Finance," Springer-Verlag, New York, 1998.  Google Scholar

[12]

Leonid Kogan, Stephen A. Ross, Jiang Wang and Mark M. Westerfield, The price impact and survival of irrational traders, Journal of Finance, 61 (2006), 195-229. doi: 10.1111/j.1540-6261.2006.00834.x.  Google Scholar

[13]

John Lintner, The valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics, 47 (1965), 13-37. doi: 10.2307/1924119.  Google Scholar

[14]

Robert C. Merton, An intertemporal capital asset pricing model, Econometrica, 41 (1973), 867-887. doi: 10.2307/1913811.  Google Scholar

[15]

Stephen A. Ross, The arbitrage theory of capital asset pricing, Journal of Economic Theory, 13 (1976), 341-360. doi: 10.1016/0022-0531(76)90046-6.  Google Scholar

[16]

Alvaro Sandroni, Do markets favor agents able to make accurate predictions?, Econometrica, 68 (2000), 1303-1341. doi: 10.1111/1468-0262.00163.  Google Scholar

[17]

William Sharpe, Capital asset prices: a theory of market equilibrium under conditions of risk, Journal of Finance, 19 (1964), 425-442. doi: 10.2307/2977928.  Google Scholar

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