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Optimal portfolios under a value-at-risk constraint

✍ Scribed by K.F.C. Yiu

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
568 KB
Volume
28
Category
Article
ISSN
0165-1889

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✦ Synopsis

This paper looks at the optimal portfolio problem when a value-at-risk constraint is imposed. This provides a way to control risks in the optimal portfolio and to fulΓΏl the requirement of regulators on market risks. The value-at-risk constraint is derived for n risky assets plus a risk-free asset and is imposed continuously over time. The problem is formulated as a constrained utility maximization problem over a period of time. The dynamic programming technique is applied to derive the Hamilton-Jacobi-Bellman equation and the method of Lagrange multiplier is used to tackle the constraint. A numerical method is proposed to solve the HJB-equation and hence the optimal constrained portfolio allocation. Under this formulation, we ΓΏnd that investments in risky assets are optimally reduced by the imposed value-at-risk constraint.

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