Continuous-time portfolio selection under ambiguity

Hanqing  Jin; Xun Yu  Zhou

doi:10.3934/mcrf.2015.5.475

Article Contents

2015, Volume 5, Issue 3: 475-488. Doi: 10.3934/mcrf.2015.5.475

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Continuous-time portfolio selection under ambiguity

Hanqing Jin^1, and
Xun Yu Zhou^1,

1.
Mathematical Institute, University of Oxford, Oxford OX2 6GG

Received: July 31, 2014

Revised: October 31, 2014

Published: August 2015

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Abstract

In a financial market, the appreciation rates of stocks are statistically difficult to estimate, and typically only some confidence intervals in which the rates reside can be estimated. In this paper we study continuous-time portfolio selection under ambiguity, in the sense that the appreciation rates are only known to be in a certain convex closed set and the portfolios are allowed to be based on only the historical stocks prices. We formulate the problem in both the expected utility and the mean--variance frameworks, and derive robust portfolios explicitly for both models.

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Mathematics Subject Classification: Primary: 91G10, 93E20; Secondary: 90B50.

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