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DYNAMIC PORTFOLIO SELECTION UNDER CAPITAL-AT-RISK WITH NO SHORT-SELLING CONSTRAINTS

Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N1N4, Canada

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ALI LARI-LAVASSANI

, 990 Biscayne Blvd Suite 503, Miami, Florida 33132, USA

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XUN LI

Department of Applied Mathematics, The Hong Kong Polytechnic University, Stanley Ho Building Hung Hom, Kowloon, Hong Kong

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, and

ANTONY WARE

Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N1N4, Canada

Corresponding author.

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https://doi.org/10.1142/S0219024911006802Cited by:3 (Source: Crossref)

Abstract

Portfolio optimization under downside risk is of crucial importance to asset managers. In this article we consider one such particular measure given by the notion of Capital at Risk (CaR), closely related to Value at Risk. We consider portfolio optimization with respect to CaR in the Black-Scholes setting with time dependent parameters and investment strategies, i.e., continuous-time portfolio optimization. We review the results from our previous work in unconstrained portfolio optimization, and then investigate and solve the corresponding problems with the additional constraint of no-short-selling. Analytical formulae are derived for the optimal strategies, and numerical examples are presented.

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