Mean-variance portfolio selection for partially observed point processes

Xiong，Jie1; Zeng，Yong2; Zhang，Shuaiqi3

2020

10.1137/19M1265491

SIAM JOURNAL ON CONTROL AND OPTIMIZATION   影响因子和分区

0363-0129

We study the mean-variance portfolio selection problem for a class of price models, which well fit the two features of time-stamped transactions data. The price process of each stock is described by a collection of partially observed point processes. They are the noisy observation of an intrinsic value process, assumed to be Markovian. However, the control problem with partial information is non-Markovian and depends on an infinite-dimensional measure-valued input. To solve the challenging problem, we first establish a separation principle, which divides the filtering and the control problems and reduces the infinite-dimensional input to finite-dimensional ones. Building upon the result of nonlinear filtering with counting process observations, we solve the control problem by employing the stochastic maximum principle for control with forward-backward SDEs developed in [SIAM J. Control Optim., 48 (2009), pp. 2945-2976]. We explicitly obtain the efficient frontier and derive the optimal strategy, which is based on the filtering estimators.

Forward-backward stochastic differential equations Market microstructure noise Maximum principle Nonlinear filtering Partial information Point process Ultrahigh frequency data

SCI ; SSCI ; CPCI-S ; EI

英语

第一

WOS:000600685600002

20204809560693

Stochastic systems ; Information filtering ; Nonlinear equations ; Nonlinear filtering

Information Theory and Signal Processing:716.1 ; Control Systems:731.1 ; Information Sources and Analysis:903.1 ; Systems Science:961

ENGINEERING

2-s2.0-85096764061

Scopus

1.Department of Mathematics,SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,China
2.Department of Mathematics and Statistics,University of Missouri at Kansas City,Kansas City,64110,United States
3.School of Mathematics,China University of Mining and Technology,Xuzhou,China

Xiong，Jie,Zeng，Yong,Zhang，Shuaiqi. Mean-variance portfolio selection for partially observed point processes[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,2020,58(6):3041-3061.

Xiong，Jie,Zeng，Yong,&Zhang，Shuaiqi.(2020).Mean-variance portfolio selection for partially observed point processes.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,58(6),3041-3061.

Xiong，Jie,et al."Mean-variance portfolio selection for partially observed point processes".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 58.6(2020):3041-3061.