Optimal Multiperiod Mean-Variance Policy Under No-Shorting Constraint

Cui, Xiangyu; Gao, Jianjun; Li, Xun; Li, Duan

doi:10.2139/ssrn.1993087

Cited by 22 publications

(23 citation statements)

References 14 publications

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“…In Section 5, we also demonstrate that Theorem provides an extension of the result in Cui et al. () for the multiperiod mean‐variance formulation with no‐shorting constraint.…”

Section: Optimal Mean‐variance Policy In a Discrete‐time Cone‐constrasupporting

confidence: 61%

“…By Lemma , we can compute

K_{t}^{+}

numerically using the penalty function method (see Appendix A of Cui et al. ()) with the initial point [1.06, 0.05, 1.11]′ as

i) {boldK}_{0}^{+} = [\begin{matrix} 1.0076 \\ 0.0044 \\ 1.0324 \end{matrix}], {boldK}_{1}^{+} = [\begin{matrix} 1.0133 \\ 0.0037 \\ 1.0373 \end{matrix}], {boldK}_{2}^{+} = [\begin{matrix} 1.0147 \\ 0.0031 \\ 1.0401 \end{matrix}]

for the multivariate normal distribution and

ii) {boldK}_{0}^{+} = [\begin{matrix} 1.0112 \\ 0.0030 \\ 1.0413 \end{matrix}], {boldK}_{1}^{+} = [\begin{matrix} 1.0201 \\ 0.0026 \\ 1.0522 \end{matrix}], {boldK}_{2}^{+} = [\begin{matrix} 1.0216 \\ 0.0039 \\ 1.0501 \end{matrix}]

for the multivariate t distribution. The optimal investment policies are

i) {boldu}_{t}^{★} false(x_{t} false) = 1.05 ((1.35 + 0.1818) 1 . 05^{t - 3} - x_{t}) {boldK}_{t}^{+} 1_{{x_{t} < 1 . 05^{(t - 3)} false(1.5318 false)}}

for the multivariate normal distribution and

ii) {boldu}_{t}^{★} false(x_{...}

…”

Section: Elimination Of Time Inconsistency In Efficiency With Portfolmentioning

confidence: 99%

See 1 more Smart Citation

Mean‐variance Policy for Discrete‐time Cone‐constrained Markets: Time Consistency in Efficiency and the Minimum‐variance Signed Supermartingale Measure

Cui

2015

Mathematical Finance

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The discrete‐time mean‐variance portfolio selection formulation, which is a representative of general dynamic mean‐risk portfolio selection problems, typically does not satisfy time consistency in efficiency (TCIE), i.e., a truncated precommitted efficient policy may become inefficient for the corresponding truncated problem. In this paper, we analytically investigate the effect of portfolio constraints on the TCIE of convex cone‐constrained markets. More specifically, we derive semi‐analytical expressions for the precommitted efficient mean‐variance policy and the minimum‐variance signed supermartingale measure (VSSM) and examine their relationship. Our analysis shows that the precommitted discrete‐time efficient mean‐variance policy satisfies TCIE if and only if the conditional expectation of the density of the VSSM (with respect to the original probability measure) is nonnegative, or once the conditional expectation becomes negative, it remains at the same negative value until the terminal time. Our finding indicates that the TCIE property depends only on the basic market setting, including portfolio constraints. This motivates us to establish a general procedure for constructing TCIE dynamic portfolio selection problems by introducing suitable portfolio constraints.

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“…In Section 5, we also demonstrate that Theorem provides an extension of the result in Cui et al. () for the multiperiod mean‐variance formulation with no‐shorting constraint.…”

Section: Optimal Mean‐variance Policy In a Discrete‐time Cone‐constrasupporting

confidence: 61%

“…By Lemma , we can compute

K_{t}^{+}

numerically using the penalty function method (see Appendix A of Cui et al. ()) with the initial point [1.06, 0.05, 1.11]′ as

i) {boldK}_{0}^{+} = [\begin{matrix} 1.0076 \\ 0.0044 \\ 1.0324 \end{matrix}], {boldK}_{1}^{+} = [\begin{matrix} 1.0133 \\ 0.0037 \\ 1.0373 \end{matrix}], {boldK}_{2}^{+} = [\begin{matrix} 1.0147 \\ 0.0031 \\ 1.0401 \end{matrix}]

for the multivariate normal distribution and

ii) {boldK}_{0}^{+} = [\begin{matrix} 1.0112 \\ 0.0030 \\ 1.0413 \end{matrix}], {boldK}_{1}^{+} = [\begin{matrix} 1.0201 \\ 0.0026 \\ 1.0522 \end{matrix}], {boldK}_{2}^{+} = [\begin{matrix} 1.0216 \\ 0.0039 \\ 1.0501 \end{matrix}]

for the multivariate t distribution. The optimal investment policies are

i) {boldu}_{t}^{★} false(x_{t} false) = 1.05 ((1.35 + 0.1818) 1 . 05^{t - 3} - x_{t}) {boldK}_{t}^{+} 1_{{x_{t} < 1 . 05^{(t - 3)} false(1.5318 false)}}

for the multivariate normal distribution and

ii) {boldu}_{t}^{★} false(x_{...}

…”

Section: Elimination Of Time Inconsistency In Efficiency With Portfolmentioning

confidence: 99%

Mean‐variance Policy for Discrete‐time Cone‐constrained Markets: Time Consistency in Efficiency and the Minimum‐variance Signed Supermartingale Measure

Cui

2015

Mathematical Finance

Self Cite

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show abstract

“…. , n, and x t be the wealth level in period t. Then, given the initial wealth x 0 , the dynamics of wealth evolves as follows, Cui et al, 2014 andLi et al, 2001). Let us consider to impose the following time cardinality constraint on admissible trading strategies,…”

Section: Problem Formulation For Time Cardinality Constrained Market mentioning

confidence: 99%

“…for dynamic MV portfolio selection by leaps and bounds, see, for example, Basak and Chabakauri (2010), Bielecki, Jin, Pliska, and Zhou (2005), Cui, Gao, Li, and Li (2014), Cui, Li, Wang, and Zhu (2012), Li, Zhou, and Lim (2001), Lim and Zhou (2002) and Zhu, Li, and Wang (2004).…”

mentioning

confidence: 99%

Time cardinality constrained mean–variance dynamic portfolio selection and market timing: A stochastic control approach

Gao

Cui

et al. 2015

Automatica

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“…Li et al [13], Cui et al [3] studied dynamic mean-variance models with no short selling constraints. Bielecki et al [2], Zhu et al [21] considered dynamic mean-variance models with no bankruptcy constraints.…”

Section: Introductionmentioning

confidence: 99%