Explicit solutions to some single-period investment problems for risky log-stable stocks

Abstract Numerical approximations are presented for the expected utility of wealth over a single time period for a small investor who proportions her or his available capital between a risk-free asset and a risky stock. The stock price is assumed to be a log-stable random variable. The utility functional is logarithmic or isoeleastic ( y a q , q

[1]  N. Y. Graham.  Perspective drawing of surfaces with hidden line elimination , 1972 .

[2]  A. Paulson,et al.  The estimation of the parameters of the stable laws , 1975 .

[3]  P. Samuelson.  Lifetime Portfolio Selection by Dynamic Stochastic Programming , 1969 .

[4]  S. Rice.  Efficient evaluation of integrals of analytic functions by the trapezoidal rule , 1973 .

[5]  Bruce D. Fielitz,et al.  Asymmetric Stable Distributions of Stock Price Changes , 1972 .

[6]  A. Barnea,et al.  A Reexamination of the Empirical Distribution of Stock Price Changes , 1973 .

[7]  H. Markowitz,et al.  The Random Character of Stock Market Prices. , 1965 .

[8]  Joseph E. Stiglitz,et al.  The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds , 1970 .

[9]  R. C. Merton,et al.  Optimum consumption and portfolio rules in a continuous - time model Journal of Economic Theory 3 , 1971 .

[10]  E. Fama,et al.  The Adjustment of Stock Prices to New Information , 1969 .

[11]  W. Ziemba,et al.  Calculation of Investment Portfolios with Risk Free Borrowing and Lending , 1974 .

[12]  E. Fama.  EFFICIENT CAPITAL MARKETS: A REVIEW OF THEORY AND EMPIRICAL WORK* , 1970 .

[13]  Paul Anthony Samuelson,et al.  Efficient Portfolio Selection for Pareto-Lévy Investments , 1967, Journal of Financial and Quantitative Analysis.

[14]  E. Fama.  The Behavior of Stock-Market Prices , 1965 .

[15]  E. Fama.  Mandelbrot and the Stable Paretian Hypothesis , 1963 .

[16]  B. Gnedenko,et al.  Limit Distributions for Sums of Independent Random Variables , 1955 .

[17]  P. Samuelson.  Mathematics of Speculative Price , 1973 .

[18]  P. Samuelson.  The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments , 1970 .

[19]  N. H. Hakansson..  OPTIMAL INVESTMENT AND CONSUMPTION STRATEGIES UNDER RISK FOR A CLASS OF UTILITY FUNCTIONS11This paper was presented at the winter meeting of the Econometric Society, San Francisco, California, December, 1966. , 1970 .

[20]  Robert A. Leitch,et al.  Estimation of Stable Law Parameters: Stock Price Behavior Application , 1975 .

[21]  K. Arrow.  Essays in the theory of risk-bearing , 1958 .

[22]  E. Fama.  Portfolio Analysis in a Stable Paretian Market , 1965 .

[23]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[24]  R. C. Merton,et al.  Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case , 1969 .

[25]  P. Samuelson.  General Proof that Diversification Pays , 1967, Journal of Financial and Quantitative Analysis.

[26]  Portfolio Selection in a Log-Stable Market , 1975 .

[27]  J. Mossin.  Optimal multiperiod portfolio policies , 1968 .

[28]  Robert C. Blattberg,et al.  A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices: Reply , 1974 .

[29]  B. Mandelbrot.  The Variation of Certain Speculative Prices , 1963 .

[30]  B. Fielitz.  Further Results on Asymmetric Stable Distributions of Stock Price Chances , 1976, Journal of Financial and Quantitative Analysis.