arXiv subjects

Xun Li

Publications and source records attributed to Xun Li.

132 records · Page 8Linked to original sources

arXiv2013

Unified Framework of Mean-Field Formulations for Optimal Multi-period Mean-Variance Portfolio Selection

The classical dynamic programming-based optimal stochastic control methods fail to cope with nonseparable dynamic optimization problems as the principle of optimality no longer applies in such situations. Among these notorious nonseparable problems, the dynamic mean-variance portfolio selection formulation had posted a great challenge to our research community until recently. A few solution methods, including the embedding scheme, have been developed in the last decade to solve the dynamic mean-variance portfolio selection formulation successfully. We propose in this paper a novel mean-field framework that offers a more efficient modeling tool and a more accurate solution scheme in tackling directly the issue of nonseparability and deriving the optimal policies analytically for the multi-period mean-variance-type portfolio selection problems.

q-fin.PM↗

arXiv2013

Continuous-time Mean-Variance Portfolio Selection with Stochastic Parameters

This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a bond. In the considered model firstly proposed by [3], the mean returns of individual assets are explicitly affected by underlying Gaussian economic factors. Using past and present information of the asset prices, a partial-information stochastic optimal control problem with random coefficients is formulated. Here, the partial information is due to the fact that the economic factors can not be directly observed. Via dynamic programming theory, the optimal portfolio strategy can be constructed by solving a deterministic forward Riccati-type ordinary differential equation and two linear deterministic backward ordinary differential equations.

q-fin.PM↗

arXiv2013

Consensus Seeking in Multi-Agent Systems with Multiplicative Measurement Noises

In this paper, the consensus problems of the continuous-time integrator systems under noisy measurements are considered. The measurement noises, which appear when agents measure their neighbors' states, are modeled to be multiplicative. By multiplication of the noises, here, the noise intensities are proportional to the absolute value of the relative states of agent and its neighbor. By using known distributed protocols for integrator agent systems, the closed-loop {system is} described in the vector form by a singular stochastic differential equation. For the fixed and switching network topologies cases, constant consensus gains are properly selected, such that mean square consensus and strong consensus can be achieved. Especially, exponential mean square convergence of agents' states to the common value is derived for the fixed topology case. In addition, asymptotic unbiased mean square average consensus and asymptotic unbiased strong average consensus are also studied. Simulations shed light on the effectiveness of the proposed theoretical results.

math.OC↗

arXiv2012

A Mixed Linear Quadratic Optimal Control Problem with a Controlled Time Horizon

A mixed linear quadratic (MLQ, for short) optimal control problem is considered. The controlled stochastic system consists of two diffusion processes which are in different time horizons. There are two control actions: a standard control action $u(\cdot)$ enters the drift and diffusion coefficients of both state equations, and a stopping time $τ$, a possible later time after the first part of the state starts, at which the second part of the state is initialized with initial condition depending on the first state. A motivation of MLQ problem from a two-stage project management is presented. It turns out that solving MLQ problem is equivalent to sequentially solve a random-duration linear quadratic (RLQ, for short) problem and an optimal time (OT, for short) problem associated with Riccati equations. In particular, the optimal cost functional can be represented via two coupled stochastic Riccati equations. Some optimality conditions for MLQ problem is therefore obtained using the equivalence among MLQ, RLQ and OT problems.

math.OC↗

arXiv2012

A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations in Infinite Horizon

A linear-quadratic (LQ, for short) optimal control problem is considered for mean-field stochastic differential equations with constant coefficients in an infinite horizon. The stabilizability of the control system is studied followed by the discussion of the well-posedness of the LQ problem. The optimal control can be expressed as a linear state feedback involving the state and its mean, through the solutions of two algebraic Riccati equations. The solvability of such kind of Riccati equations is investigated by means of semi-definite programming method.

math.OC↗

arXiv2007

Continuous-time mean-variance efficiency: the 80% rule

This paper studies a continuous-time market where an agent, having specified an investment horizon and a targeted terminal mean return, seeks to minimize the variance of the return. The optimal portfolio of such a problem is called mean-variance efficient à la Markowitz. It is shown that, when the market coefficients are deterministic functions of time, a mean-variance efficient portfolio realizes the (discounted) targeted return on or before the terminal date with a probability greater than 0.8072. This number is universal irrespective of the market parameters, the targeted return and the length of the investment horizon.

math.PR↗