Optimal Strategies for Prudent Investors

Roberto Baviera, Michele Pasquini, Maurizio Serva and Angelo Vulpiani
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Roberto Baviera: Dipartimento di Fisica, Università dell'Aquila, and Istituto Nazionale Fisica della Materia Via Vetoio I-67010 Coppito, L'Aquila, Italy
Michele Pasquini: Dipartimento di Matematica, Università dell'Aquila, and Istituto Nazionale Fisica della Materia Via Vetoio, I-67010 Coppito, L'Aquila, Italy
Maurizio Serva: Dipartimento di Matematica, Università dell'Aquila, and Istituto Nazionale Fisica della Materia Via Vetoio, I-67010 Coppito, L'Aquila, Italy
Angelo Vulpiani: Dipartimento di Fisica, Università di Roma "La Sapienza", and Istituto Nazionale Fisica della Materia P.le A. Moro 2, I-00185 Roma, Italy

International Journal of Theoretical and Applied Finance (IJTAF), 1998, vol. 01, issue 04, 473-486

Abstract: We consider a stochastic model of investment on an asset in a stock market for a prudent investor. she decides to buy permanent goods with a fraction α of the maximum amount of money owned in her life in order that her economic level never decreases. The optimal strategy is obtained by maximizing the exponential growth rate for a fixed α. We derive analytical expressions for the typical exponential growth rate of the capital and its fluctuations by solving an one-dimensional random walk with drift.

Date: 1998
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DOI: 10.1142/S0219024998000254

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