# Optimal Dynamic Portfolio with Mean-CVaR Criterion

*Jing Li* and
*Mingxin Xu*

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Jing Li: Federal Reserve Bank of New York, New York, NY 10045, USA

*Risks*, 2013, vol. 1, issue 3, 1-29

**Abstract:**
Value-at-risk (VaR) and conditional value-at-risk (CVaR) are popular risk measures from academic, industrial and regulatory perspectives. The problem of minimizing CVaR is theoretically known to be of a Neyman–Pearson type binary solution. We add a constraint on expected return to investigate the mean-CVaR portfolio selection problem in a dynamic setting: the investor is faced with a Markowitz type of risk reward problem at the final horizon, where variance as a measure of risk is replaced by CVaR. Based on the complete market assumption, we give an analytical solution in general. The novelty of our solution is that it is no longer the Neyman–Pearson type, in which the final optimal portfolio takes only two values. Instead, in the case in which the portfolio value is required to be bounded from above, the optimal solution takes three values; while in the case in which there is no upper bound, the optimal investment portfolio does not exist, though a three-level portfolio still provides a sub-optimal solution.

**Keywords:** conditional value-at-risk; mean-CVaR portfolio optimization; risk minimization; Neyman–Pearson problem (search for similar items in EconPapers)

**JEL-codes:** C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)

**Date:** 2013

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** View citations in EconPapers (3)

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**Persistent link:** https://EconPapers.repec.org/RePEc:gam:jrisks:v:1:y:2013:i:3:p:119-147:d:30341

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