arXiv subjects

Jiaqin Wei

Publications and source records attributed to Jiaqin Wei.

6 recordsLinked to original sources

arXiv2026

Equilibrium strategies for stochastic control problems with higher-order moments and applications to portfolio selection

In this paper we derive a novel characterization result for time-consistent stochastic control problems with higher-order moments, originally formulated by Wang et al. [SIAM J. Control. Optim., 63 (2025), 1560--1589], and newly explore many solvable instances including a mean-variance-excess kurtosis portfolio selection problem. By improving an asymptotic result of the variational process for the uniform boundedness and integrability properties, we obtain both the sufficiency and necessity of an equilibrium condition for an open-loop Nash equilibrium control (ONEC). This condition is simply formulated by the diagonal processes of a flow of backward stochastic differential equations (BSDEs) whose data do not necessarily satisfy the usual square-integrability condition. In particular, for linear controlled dynamics with deterministic parameters, we show that the ONEC can be derived by solving a polynomial algebraic equation under a class of nonlinear objective functions. Interestingly, the mean-variance equilibrium strategy is an ONEC for our general higher-order moment problem if and only if a homogeneity condition holds. Additionally, in the case with random parameters, we characterize the ONEC by finitely many BSDEs with a recurrence relation. As an intuitive illustration, the solution to the mean-variance-skewness problems is given by a quadratic BSDE.

math.OC↗

arXiv2025

On stochastic control problems with higher-order moments

In this paper, we focus on a class of time-inconsistent stochastic control problems, where the objective function includes the mean and several higher-order central moments of the terminal value of state. To tackle the time-inconsistency, we seek both the closed-loop and the open-loop Nash equilibrium controls as time-consistent solutions. We establish a partial differential equation (PDE) system for deriving a closed-loop Nash equilibrium control, which does not include the equilibrium value function and is different from the extended Hamilton-Jacobi-Bellman (HJB) equations as in Björk et al. (Finance Stoch. 21: 331-360, 2017). We show that our PDE system is equivalent to the extended HJB equations that seems difficult to be solved for our higher-order moment problems. In deriving an open-loop Nash equilibrium control, due to the non-separable higher-order moments in the objective function, we make some moment estimates in addition to the standard perturbation argument for developing a maximum principle. Then, the problem is reduced to solving a flow of forward-backward stochastic differential equations. In particular, we investigate linear controlled dynamics and some objective functions affine in the mean. The closed-loop and the open-loop Nash equilibrium controls are identical, which are independent of the state value, random path and the preference on the odd-order central moments. By sending the highest order of central moments to infinity, we obtain the time-consistent solutions to some control problems whose objective functions include some penalty functions for deviation.

q-fin.MF↗

arXiv2024

A hybrid deep learning method for finite-horizon mean-field game problems

This paper develops a new deep learning algorithm to solve a class of finite-horizon mean-field games. The proposed hybrid algorithm uses Markov chain approximation method combined with a stochastic approximation-based iterative deep learning algorithm. Under the framework of finite-horizon mean-field games, the induced measure and Monte-Carlo algorithm are adopted to establish the iterative mean-field interaction in Markov chain approximation method and deep learning, respectively. The Markov chain approximation method plays a key role in constructing the iterative algorithm and estimating an initial value of a neural network, whereas stochastic approximation is used to find accurate parameters in a bounded region. The convergence of the hybrid algorithm is proved; two numerical examples are provided to illustrate the results.

math.OC↗

arXiv2024

Time-Consistent Portfolio Selection for Rank-Dependent Utilities in an Incomplete Market

We investigate the portfolio selection problem for an agent with rank-dependent utility in an incomplete financial market. For a constant-coefficient market and CRRA utilities, we characterize the deterministic strict equilibrium strategies. In the case of time-invariant probability weighting function, we provide a comprehensive characterization of the deterministic strict equilibrium strategy. The unique non-zero equilibrium, if exists, can be determined by solving an autonomous ODE. In the case of time-variant probability weighting functions, we observe that there may be infinitely many non-zero deterministic strict equilibrium strategies, which are derived from the positive solutions to a nonlinear singular ODE. By specifying the maximal solution to the singular ODE, we are able to identify all the positive solutions. In addition, we address the issue of selecting an optimal strategy from the numerous equilibrium strategies available.

q-fin.MF↗

arXiv2013

On the Dividend Strategies with Non-Exponential Discounting

In this paper, we study the dividend strategies for a shareholder with non-constant discount rate in a diffusion risk model. We assume that the dividends can only be paid at a bounded rate and restrict ourselves to the Markov strategies. This is a time inconsistent control problem. The extended HJB equation is given and the verification theorem is proved for a general discount function. Considering the pseudo-exponential discount functions (Type I and Type II), we get the equilibrium dividend strategies and the equilibrium value functions by solving the extended HJB equations.

q-fin.PM↗

arXiv2013

Mean-Variance Asset-Liability Management with State-Dependent Risk Aversion

In this paper, we consider the asset-liability management under the mean-variance criterion. The financial market consists of a risk-free bond and a stock whose price process is modeled by a geometric Brownian motion. The liability of the investor is uncontrollable and is modeled by another geometric Brownian motion. We consider a specific state-dependent risk aversion which depends on a power function of the liability. By solving a flow of FBSDEs with bivariate state process, we obtain the equilibrium strategy among all the open-loop controls for this time-inconsistent control problem. It shows that the equilibrium strategy is a feedback control of the liability.

q-fin.RM↗