arXiv subjects

Kexin Shao

Publications and source records attributed to Kexin Shao.

3 recordsLinked to original sources

arXiv2026

Extended Graphon Mean-Field Games in Discrete Time

In this paper, we study games involving a continuum of heterogeneous players in the discrete-time setting with finite state spaces and continuous action spaces. We introduce a new model that incorporates joint state-action interactions within the graphon-weighted aggregate, described by a coupled forward-backward system. We establish the existence of graphon mean-field equilibria and characterize them through this forward-backward system. Additionally, we provide uniqueness results under monotonicity and contraction conditions. To illustrate the practical relevance of our framework, we solve an example of portfolio liquidation with price impact. We provide numerical results for three different graphons and two different initial distributions, illustrating the impact of the network's structure and the distribution heterogeneity on the distribution and the policy.

math.OC↗

arXiv2023

Maximal Martingale Wasserstein Inequality

In this note, we complete the analysis of the Martingale Wasserstein Inequality started in arXiv:2011.11599 by checking that this inequality fails in dimension $d\ge 2$ when the integrability parameter $ρ$ belongs to $[1,2)$ while a stronger Maximal Martingale Wasserstein Inequality holds whatever the dimension $d$ when $ρ\ge 2$.

math.PR↗

arXiv2023

Non-decreasing martingale couplings

For many examples of couples $(μ,ν)$ of probability measures on the real line in the convex order, we observe numerically that the Hobson and Neuberger martingale coupling, which maximizes for $ρ=1$ the integral of $|y-x|^ρ$ with respect to any martingale coupling between $μ$ and $ν$, is still a maximizer for $ρ\in(0,2)$ and a minimizer for $ρ>2$. We investigate the theoretical validity of this numerical observation and give rather restrictive sufficient conditions for the property to hold. We also exhibit couples $(μ,ν)$ such that it does not hold. The support of the Hobson and Neuberger coupling is known to satisfy some monotonicity property which we call non-decreasing. We check that the non-decreasing property is preserved for maximizers when $ρ\in(0,1]$. In general, there exist distinct non-decreasing martingale couplings, and we find some decomposition of $ν$ which is in one-to-one correspondence with martingale couplings non-decreasing in a generalized sense.

math.PR↗