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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 784275, 10 pages
Research Article

Pessimistic Portfolio Choice with One Safe and One Risky Asset and Right Monotone Probability Difference Order

1School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, China
2School of Science, Jiujiang University, Jiujiang, Jiangxi 332005, China
3School of Business, East China University of Science and Technology, Shanghai 200237, China
4School of Finance, Renmin University of China, Beijing 100872, China

Received 1 June 2013; Revised 10 October 2013; Accepted 14 October 2013

Academic Editor: Francesco Pellicano

Copyright © 2013 Jiangfeng Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


As is well known, a first-order dominant deterioration in risk does not necessarily cause a risk-averse investor to reduce his holdings of that deteriorated asset under the expected utility framework, even in the simplest portfolio setting with one safe asset and one risky asset. The purpose of this paper is to derive conditions on shifts in the distribution of the risky asset under which the counterintuitive conclusion above can be overthrown under the rank-dependent expected utility framework, a more general and prominent alternative of the expected utility. Two new criterions of changes in risk, named the monotone probability difference (MPD) and the right monotone probability difference (RMPD) order, are proposed, which is a particular case of the first stochastic dominance. The relationship among MPD, RMPD, and the other two important stochastic orders, monotone likelihood ratio (MLR) and monotone probability ratio (MPR), is examined. A desired comparative statics result is obtained when a shift in the distribution of the risky asset satisfies the RMPD criterion.