#### DMCA

## Unified Framework of Mean-Field Formulations for Optimal Multi-period Mean-Variance Portfolio Selection (2014)

Citations: | 1 - 0 self |

### Citations

2834 |
Portfolio selection
- Markowitz
- 1952
(Show Context)
Citation Context ...[10], Zhu et al. [28]), reformulate them as discrete-time linear-quadratic control problems of a mean-field type, and derive their optimal strategies with improved solution qualities. Since Markowitz =-=[18]-=- published his seminal work on the mean-variance portfolio selection sixty years ago, the mean-risk portfolio selection framework has become one of the most significant ingredients in the modern finan... |

180 | Backward stochastic differential equations and integral-partial differential equations
- Barles, Buckdahn, et al.
- 1997
(Show Context)
Citation Context ...blems, Yong [26] introduced a system of two Riccati equations to solve the problem. Representative works in mean-field include, but not limited to, Mckean [19], Dawson [12], Chan [7], Buckdahn et al. =-=[4]-=-, Borkar and Kumar [2], Crisan and Xiong [11], Andersson and Djehiche [1], Buckdahn et al. [3], Meyer-Brandis et al. [21], Nourian et al. [22] and Yong [26]. Despite active research efforts on mean-fi... |

120 |
Foundations of kinetic theory
- Kac
- 1956
(Show Context)
Citation Context ...eld). This critical feature differentiates the mean-variance problem from standard stochastic control problems. The theory of the mean-field stochastic differential equation can be traced back to Kac =-=[14]-=- who presented the McKean-Vlasov stochastic differential equation motivated by a stochastic toy model for the Vlasov kinetic equation of plasma. Since then, the research on related topics and their ap... |

87 | An Analytical Derivation of the Efficient Portfolio Frontier.
- Merton
- 1972
(Show Context)
Citation Context ... denotes the trade-off between the two conflicting objectives of maximizing expected return and minimizing the risk. The optimal portfolio strategy and solution scheme of (MVs) can be found in Merton =-=[20]-=- when shorting is allowed and in Markowitz [18] when shorting is prohibited. However, the extension to a dynamic version of mean-variance portfolio selection was blocked for four decades until recentl... |

67 |
Approximation Pricing and the Variance-Optimal Martingale Measure,
- Schweizer
- 1996
(Show Context)
Citation Context ...y his/her portfolio under a quadratic objective function. Problem (MVH(m)) has been well studied and can be solved by LQSC theory (see Li et al. [17]), martingale/convex duality theory (see Schweizer =-=[23]-=-, Xia and Yan [25]) and sequential regression method (see Černý and Kellsen [6]). 3 In all the literature mentioned above, a static optimization procedure is always necessary to identify an optimal ... |

65 | Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation.
- Li, Ng
- 2000
(Show Context)
Citation Context ...hinese University of Hong Kong, Hong Kong, China. E-mail: dli@se.cuhk.edu.hk. 1 challenging, yet practically important, portfolio selection models over a finite-time investment horizon (see Li and Ng =-=[16]-=-, Costa and Nabholz [10], Zhu et al. [28]), reformulate them as discrete-time linear-quadratic control problems of a mean-field type, and derive their optimal strategies with improved solution qualiti... |

61 |
A class of Markov processes associated with nonlinear parabolic equations
- McKean
- 1907
(Show Context)
Citation Context ...eld forward stochastic LQ optimal control problems, Yong [26] introduced a system of two Riccati equations to solve the problem. Representative works in mean-field include, but not limited to, Mckean =-=[19]-=-, Dawson [12], Chan [7], Buckdahn et al. [4], Borkar and Kumar [2], Crisan and Xiong [11], Andersson and Djehiche [1], Buckdahn et al. [3], Meyer-Brandis et al. [21], Nourian et al. [22] and Yong [26]... |

46 | Continuous-time mean-variance portfolio selection:a stochastic
- Zhou, Li
- 2000
(Show Context)
Citation Context ...pply. We now briefly summarize the main approaches in the current literature to overcome the difficulty resulted from the nonseparability. Adopting an embedding scheme, Li and Ng [16] and Zhou and Li =-=[27]-=- considered the following family of auxiliary problems, A(ω, λ), parameterized in parameter λ, A(ω, λ) min u E(ωx2T − λxT ), s.t. xT = x0 + {ut • St} | T−1 t=0 . Note that problem A(ω, λ) is a separab... |

41 |
Critical dynamics and fluctuations for a mean-field model of cooperative behavior,
- Dawson
- 1983
(Show Context)
Citation Context ...tochastic LQ optimal control problems, Yong [26] introduced a system of two Riccati equations to solve the problem. Representative works in mean-field include, but not limited to, Mckean [19], Dawson =-=[12]-=-, Chan [7], Buckdahn et al. [4], Borkar and Kumar [2], Crisan and Xiong [11], Andersson and Djehiche [1], Buckdahn et al. [3], Meyer-Brandis et al. [21], Nourian et al. [22] and Yong [26]. Despite act... |

36 | Stochastic linear quadratic optimal control problems
- Chen, Yong
(Show Context)
Citation Context ... engineering. This new direction, however, requires new analytical tools and solution techniques. For instance, in a recent research on mean-field forward stochastic LQ optimal control problems, Yong =-=[26]-=- introduced a system of two Riccati equations to solve the problem. Representative works in mean-field include, but not limited to, Mckean [19], Dawson [12], Chan [7], Buckdahn et al. [4], Borkar and ... |

26 |
B.: A maximum principle for SDE’s of mean-field type
- Andersson, Djehiche
- 2010
(Show Context)
Citation Context ...e problem. Representative works in mean-field include, but not limited to, Mckean [19], Dawson [12], Chan [7], Buckdahn et al. [4], Borkar and Kumar [2], Crisan and Xiong [11], Andersson and Djehiche =-=[1]-=-, Buckdahn et al. [3], Meyer-Brandis et al. [21], Nourian et al. [22] and Yong [26]. Despite active research efforts on mean-field in recent years, the topic of multiperiod models in discrete-time rem... |

25 | Dynamic Mean–Variance Portfolio Selection with No-Shorting Constraints, - LI, ZHOU, et al. - 2001 |

19 | A geometric approach to multiperiod mean variance optimization of assets and liabilities.
- Leippold, Trojani, et al.
- 2004
(Show Context)
Citation Context ...(see Çelikyurt and Özekici [5]), a generalized mean-variance model with risk control over bankruptcy (see Zhu et al. [28]), and dynamic mean-variance asset-liability management (see Leippold et al. =-=[15]-=-, Chiu and Li [9], Chen and Yang [8]). By introducing an auxiliary variable d and an equality constraint E(xT ) = d for the expected terminal wealth, Li et al. [17] paved the road to study the followi... |

18 |
A general stochastic maximum principle for SDEs of mean-field type,”
- Buckdahn, Djehiche, et al.
- 2011
(Show Context)
Citation Context ...tive works in mean-field include, but not limited to, Mckean [19], Dawson [12], Chan [7], Buckdahn et al. [4], Borkar and Kumar [2], Crisan and Xiong [11], Andersson and Djehiche [1], Buckdahn et al. =-=[3]-=-, Meyer-Brandis et al. [21], Nourian et al. [22] and Yong [26]. Despite active research efforts on mean-field in recent years, the topic of multiperiod models in discrete-time remains a relatively une... |

16 | Approximate McKean-Vlasov representations for a class of SPDEs. - Crisan, Xiong - 2009 |

12 |
A meanfield stochastic maximum principle via Malliavin calculus,”
- Meyer-Brandis, Øksendal, et al.
- 2012
(Show Context)
Citation Context ...nclude, but not limited to, Mckean [19], Dawson [12], Chan [7], Buckdahn et al. [4], Borkar and Kumar [2], Crisan and Xiong [11], Andersson and Djehiche [1], Buckdahn et al. [3], Meyer-Brandis et al. =-=[21]-=-, Nourian et al. [22] and Yong [26]. Despite active research efforts on mean-field in recent years, the topic of multiperiod models in discrete-time remains a relatively unexplored subject where the m... |

11 |
Multiperiod portfolio optimization models in stochastic markets using the mean–variance approach.
- Celikyurt, Özekici
- 2007
(Show Context)
Citation Context ...del with intertemporal restrictions (see Costa and Nabholz [10]), multi-period mean-variance model in a stochastic market whose evolution is governed by a Markovian chain (see Çelikyurt and Özekici =-=[5]-=-), a generalized mean-variance model with risk control over bankruptcy (see Zhu et al. [28]), and dynamic mean-variance asset-liability management (see Leippold et al. [15], Chiu and Li [9], Chen and ... |

11 |
Asset and liability management under a continuous-time mean-variance optimization framework,”
- Chiu, Li
- 2006
(Show Context)
Citation Context ...d Özekici [5]), a generalized mean-variance model with risk control over bankruptcy (see Zhu et al. [28]), and dynamic mean-variance asset-liability management (see Leippold et al. [15], Chiu and Li =-=[9]-=-, Chen and Yang [8]). By introducing an auxiliary variable d and an equality constraint E(xT ) = d for the expected terminal wealth, Li et al. [17] paved the road to study the following slightly modif... |

8 |
Dynamics of the McKean-Vlasov equation
- Chan
- 1994
(Show Context)
Citation Context ...Q optimal control problems, Yong [26] introduced a system of two Riccati equations to solve the problem. Representative works in mean-field include, but not limited to, Mckean [19], Dawson [12], Chan =-=[7]-=-, Buckdahn et al. [4], Borkar and Kumar [2], Crisan and Xiong [11], Andersson and Djehiche [1], Buckdahn et al. [3], Meyer-Brandis et al. [21], Nourian et al. [22] and Yong [26]. Despite active resear... |

7 |
Risk control over bankruptcy in dynamic portfolio selection: A generalized mean-variance formulation.
- Zhu, Li, et al.
- 2004
(Show Context)
Citation Context ..., China. E-mail: dli@se.cuhk.edu.hk. 1 challenging, yet practically important, portfolio selection models over a finite-time investment horizon (see Li and Ng [16], Costa and Nabholz [10], Zhu et al. =-=[28]-=-), reformulate them as discrete-time linear-quadratic control problems of a mean-field type, and derive their optimal strategies with improved solution qualities. Since Markowitz [18] published his se... |

6 |
Mean-field limit in portfolio optimization
- Borkar, Kumar
- 2010
(Show Context)
Citation Context ...duced a system of two Riccati equations to solve the problem. Representative works in mean-field include, but not limited to, Mckean [19], Dawson [12], Chan [7], Buckdahn et al. [4], Borkar and Kumar =-=[2]-=-, Crisan and Xiong [11], Andersson and Djehiche [1], Buckdahn et al. [3], Meyer-Brandis et al. [21], Nourian et al. [22] and Yong [26]. Despite active research efforts on mean-field in recent years, t... |

6 | Markowitz’s mean-variance asset-liability management with regime switching: A continuous-time model.
- Chen, Yang, et al.
- 2008
(Show Context)
Citation Context ...generalized mean-variance model with risk control over bankruptcy (see Zhu et al. [28]), and dynamic mean-variance asset-liability management (see Leippold et al. [15], Chiu and Li [9], Chen and Yang =-=[8]-=-). By introducing an auxiliary variable d and an equality constraint E(xT ) = d for the expected terminal wealth, Li et al. [17] paved the road to study the following slightly modified, albeit equival... |

5 |
Multiperiod mean-variance optimization with intertemporal restrictions,”
- Costa, Nabholz
- 2007
(Show Context)
Citation Context ...g Kong, Hong Kong, China. E-mail: dli@se.cuhk.edu.hk. 1 challenging, yet practically important, portfolio selection models over a finite-time investment horizon (see Li and Ng [16], Costa and Nabholz =-=[10]-=-, Zhu et al. [28]), reformulate them as discrete-time linear-quadratic control problems of a mean-field type, and derive their optimal strategies with improved solution qualities. Since Markowitz [18]... |

5 |
The mean-variance investment problem in a constrained financial market.
- Sun, Wang
- 2006
(Show Context)
Citation Context ...dure is always necessary to identify an optimal parameter in the parameterized auxiliary problem A(ω, λ), (L(λ)) or (MVH(m)). Actually, based on the pure geometric structure of (MV (ω)), Sun and Wang =-=[24]-=- proved that the optimal terminal wealth x∗T takes the following form, x∗T = x0 + 1 2ω 1 E(1− {ϕ∗t • St} | T−1 t=0 ) {ϕ∗t • St} | T−1 t=0 , where ϕ∗ is the policy of the following particular mean-vari... |

4 |
2006): Markowitz’s portfolio optimization in an incomplete market
- Xia, Yan
(Show Context)
Citation Context ...o under a quadratic objective function. Problem (MVH(m)) has been well studied and can be solved by LQSC theory (see Li et al. [17]), martingale/convex duality theory (see Schweizer [23], Xia and Yan =-=[25]-=-) and sequential regression method (see Černý and Kellsen [6]). 3 In all the literature mentioned above, a static optimization procedure is always necessary to identify an optimal parameter in the p... |

3 |
Nash, Social and Centralized Solutions to Consensus Problems via Mean Field Control Theory
- NOURIAN, CAINES, et al.
- 2013
(Show Context)
Citation Context ...ed to, Mckean [19], Dawson [12], Chan [7], Buckdahn et al. [4], Borkar and Kumar [2], Crisan and Xiong [11], Andersson and Djehiche [1], Buckdahn et al. [3], Meyer-Brandis et al. [21], Nourian et al. =-=[22]-=- and Yong [26]. Despite active research efforts on mean-field in recent years, the topic of multiperiod models in discrete-time remains a relatively unexplored subject where the mean-field modeling sc... |

1 |
Hedging by sequential regressions revisted
- Černý, Kellsen
(Show Context)
Citation Context ...n well studied and can be solved by LQSC theory (see Li et al. [17]), martingale/convex duality theory (see Schweizer [23], Xia and Yan [25]) and sequential regression method (see Černý and Kellsen =-=[6]-=-). 3 In all the literature mentioned above, a static optimization procedure is always necessary to identify an optimal parameter in the parameterized auxiliary problem A(ω, λ), (L(λ)) or (MVH(m)). Act... |

1 |
Modern Portfolio Thoery and Investment Analysis
- Gruber, Brown, et al.
- 2007
(Show Context)
Citation Context ... an example of constructing a pension fund consisting of S&P 500 (SP), the index of Emerging Market (EM), Small Stock (MS) of U.S market and a bank account. Based on the data provided in Elton et al. =-=[13]-=-, the expected values, variances and correlations of the annual return rates of these three indices are given in Table 1. Table 1: Data for the asset allocation example SP EM MS Expected Return 14% 16... |