This paper studies a general class of time-inconsistent stochastic control problems under ambiguous covariance matrix. The time-inconsistency is caused in various ways by a general objective functional and thus the associated control problem does not admit Bellman's principle of optimality....

This paper investigates the investment and reinsurance problem in the presence of stochastic volatility for an ambiguity-averse insurer (AAI) with a general concave utility function. The AAI concerns about model uncertainty and seeks for an optimal robust decision. We consider a Brownian motion...

This paper considers the non-zero-sum stochastic differential game problem between two ambiguity-averse insurers (AAIs) who encounter model uncertainty and seek the optimal investment and reinsurance decision under relative performance concerns. Each AAI invests in a risky asset and a risk-free...

This paper studies stochastic linear-quadratic control problems for an ambiguity-adverse agent with a time-inconsistent objective. We allow the agent to incorporate disturbances into the state's drift or choose an alternative model among a set of models equivalent to the reference model, to...

Modern day trading practice resembles a thought experiment, where investors imagine various possibilities of future stock market and invest accordingly. Generative adversarial network (GAN) is highly relevant to this trading practice in two ways. First, GAN generates synthetic data by a neural...

This paper establishes a general analytical framework for continuous-time stochastic control problems for an ambiguity-averse agent (AAA) with time-inconsistent preference, where the control problems do not satisfy Bellman's principle of optimality. The AAA is concerned about model uncertainty...

This paper establishes a general analytical framework for the impulse controls of the diffusion processes driven by multidimensional G-Brownian motion. We propose new G-quasi-variational inequalities (G-QVI) and we provide a verification theorem to link a classical (smooth) solution of the G-QVI...