Abstract
This study focuses on the problem of investors in optimising dynamic asset allocation to maximise expected utility under the value-at-risk (VaR) constraint. Although Basak and Shapiro presented this topic, they assumed a complete market and employed the martingale approach to determine a dynamic asset allocation strategy. However, a complete market does not exist in the real world and the martingale approach is not suitable for portfolio selection. Consequently, this study relaxes these limitations and firstly provides a solving method to derive the dynamic asset allocation under the VaR constraint. A simple case and a general case of derivation of optimal dynamic asset allocation are explored. A continuous probability distribution also can be approximated by the discrete probability distribution discussed in this study.
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