Risk Management in Finance and Logistics by Chunhui Xu & Takayuki Shiina
Author:Chunhui Xu & Takayuki Shiina
Language: eng
Format: epub
ISBN: 9789811303173
Publisher: Springer Singapore
(5.19)
where d = V aR α(x).
Portfolio selection model (5.18) is equivalent to the following LP.
(5.20)
where R(x, j) is the jth scenario of the profit rate of portfolio x, which is calculated with formula (4.36) in Chap. 4.
When the profit rates of components follow the normal distribution, CVaR minimization model becomes a nonlinear programming.
According to (4.54), CVaR of portfolio x is given by the following formula,
where σ(x), l(x) is the standard deviation and mean of the loss rate of the portfolio, respectively, which are given in (4.43).
CVaR minimization in such a case is a conventional NLP, which can be solved using common algorithms for NLP.
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