“Topological Chaos in Oligopoly Competition” (2025), Economics Letters, Vol.252, No.112330, joint with Xiaoliang Li

Abstract:
This letter demonstrates that oligopoly competition can exhibit topological chaos by applying Mitra’s sufficient condition. To overcome the computational challenges arising from the lack of a simple closed-form expression for the modal point, we develop a resultant-based method. Our results show that, for a sufficiently large number of firms, there must exist parameter values that guarantee topological chaos.

Available at SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5195101

“Modeling Green Reputation Decisions in a Nonlinear Cournot Duopoly of Carbon Emission Abatement” （2025），Economic Modelling, joint with Xiaoliang Li and Shuie Sun

Abstract:
In response to consumer environmental awareness and carbon taxation, we develop a nonlinear Cournot duopoly model to examine how firms make green reputation decisions. Using symbolic computation methods, we analyze equilibrium strategies in both static and dynamic settings. Our results show that a firm’s emission abatement effort increases with its basic production cost, green efficiency, and carbon tax rate. Under nonlinear demand, less productive firms may exert greater effort to improve their green reputation, a phenomenon not observed under linear demand. Numerical simulations also show that excessive carbon taxes or low green efficiency can disrupt market equilibrium. Our study offers policymakers and business practitioners practical insights into how regulatory incentives and consumer preferences shape firms’ green strategies. The proposed framework supports the development of environmental policies that foster green transformation and support long-term market stability.

“Green Goodwill in a Monopolistic Market: A Dynamic Game Approach to Carbon Emission Abatement and Market Stability” (forthcoming), Finance Research Letters, joint with Yuhao Cheng, Xiaoliang Li and Shuie Sun

Abstract:
This paper investigates carbon emission abatement in a monopolistic market through a novel dynamic game framework, where the monopolist builds green goodwill and consumers exhibit green awareness. We derive a closed-form equilibrium solution and show that the monopolist’s green goodwill is positively influenced by both consumers’ green awareness and the carbon tax rate, while it is negatively affected by the green cost level. Comparative static analysis explores the impacts on product prices, consumer and producer surplus, social welfare, and total carbon emissions. Notably, our findings reveal that carbon taxation consistently reduces total carbon emissions. However, increasing consumers’ green awareness or advancing green technologies reduces emissions only when the market size surpasses a certain threshold. Additionally, our stability analysis indicates that lower consumer green awareness or higher carbon tax rates enhance market stability, whereas extreme levels-either very high or very low-of green costs may induce market fluctuations.

“Influence of Price Elasticity of Demand on Monopoly Games under Different Returns to Scale” (2025), Mathematics and Computers in Simulation, Vol. 233, pp. 75-98, joint with Xiaoliang Li and Jing Yang

Abstract:
This paper examines a monopoly market featured by a general isoelastic demand function. Assuming that the monopolist’s cost function is quadratic, we investigate the influence of the price elasticity of demand on the behavior of monopoly games under various (decreasing, constant, and increasing) returns to scale. Note that the assumption of a general isoelastic demand function and a quadratic cost function results in the equilibrium equation becoming transcendental, which makes the closed-form solutions unattainable. To overcome this obstacle, we adopt an innovative approach that utilizes the special structure of the marginal revenue and the marginal cost to conduct the comparative static analysis and the stability analysis. This paper also introduces two boundedly rational dynamic models based on different (gradient and LMA) mechanisms of adjusting the output. Our findings reveal that the LMA model is more stable in both the parameter space and the state space than the gradient model. In particular, it is proved that the unique non-vanishing equilibrium of the LMA model is globally asymptotically stable.

Available at SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4945483

“How Much is the Gap? — Efficient Overnight Jump Risk-Adjusted Valuation of Leveraged Certificates” (2017), Quantitative Finance, Vol. 17, No. 9, pp. 1387-1401, joint with Matthias Thul

Abstract:
This paper develops a novel and highly efficient numerical algorithm for the gap risk-adjusted valuation of leveraged certificates. The existing literature relies exclusively on Monte Carlo simulations for this purpose. These are not sufficiently fast to be used in a market making environment where issuers need to compute thousands of price updates per second. By valuing leveraged certificates as multi-window barrier options, we explicitly model jumps that occur at deterministically known times, such as between the exchange closing and re-opening. Our algorithm combines the one-day transition probability with Simpson’s numerical integration rule. This yields a backward induction scheme that requires a significantly coarser spacial and time grid than finite difference methods. We demonstrate its robustness and accuracy through Monte Carlo simulations.

Published version: http://www.tandfonline.com/doi/full/10.1080/14697688.2016.1276299
Preprint available at SSRN: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2388734

Presented or Accepted for Presentation at:

• 9th World Congress of the Bachelier Finance Society, July 2016, New York