Unreasonable rationality?

Article Abstract:

An Arrow-Debreu framework is used to examine how changes in the optimal fraction of wealth invested in a security are affected by exogenous changes in security returns and wealth. The analysis points to the counterintuitive but totally rational conclusion that fractional demands may remain unaffected or may even decline when security returns exogenously increase. It is shown that this can happen without disturbing the wealth effect. These results are applied to ordinary securities and a complete analytical solution is developed. It is shown that portfolio managers should be cautious in concluding that holdings in any particular stock should be increased or decreased based solely on the information that the return from holding an underlying pure security will improve.

Evaluation, Portfolio management, Investments, Rationalism, Decision theory

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Stochastic shortest path problems with piecewise-linear concave utility functions

Article Abstract:

A study was conducted to analyze a stochastic shortest path problem wherein the arc lengths are independent random variables supporting a normal distribution. The optimal path optimizes the expected utility function that was piecewise-linear, concave and nondecreasing. Two algorithms were designed to determine solutions to large problem instances. The algorithms were then integrated in labelling processesand their performance evaluated in a set of medium-sized problems in FORTRAN. Results indicated that the performance of the algorithms correlates with the curvature of the piecewise linear utility function. The findings also showed the effectiveness of the algorithms in determining solutions to large problems.

Stochastic processes, Utility theory, Utility functions

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