Research.

Studies American option pricing when volatility is driven by a slowly varying stochastic factor. An asymptotic expansion yields analytical approximations for both the option value and optimal exercise boundary; a Kim-type integral equation improves the leading-order computation, and explicit error analysis provides accuracy guarantees.

Develops a nonlocal BSDE-based feedback-control approach to dynamic mean-variance asset allocation in general incomplete markets.

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Introduces Q-world-informed neural networks (QINN), which balance empirical option-price fitting against PDE consistency, and a model-free extension, QINN², in which a neural network learns the volatility input to a Black–Scholes PDE backbone. Experiments across Black–Scholes, CEV, Heston and 3/2 models demonstrate robust pricing and parameter-learning performance.

Develops an LM-type test of a random-walk null hypothesis for functional time series, without relying on functional principal component analysis or a finite-dimensional unit-root subspace. The work establishes asymptotic validity and consistency, and studies the test through simulations and intraday stock-price curves.

Develops two analytical approximation frameworks for American option prices and optimal exercise strategies under regime-switching models: one perturbed around a Black–Scholes solution and one tailored to short-tenor options. Explicit error bounds support the approximations, while numerical results illustrate their accuracy and efficiency.

Formulates robust, time-inconsistent linear-quadratic control as a stochastic differential game. Sufficient equilibrium conditions are developed through spike variations, with mean-variance examples exploring how state- and control-dependent ambiguity aversion changes the resulting decisions.

Combines a hidden Markov model with Wasserstein generative adversarial networks to simulate multivariate stock returns across market regimes. A regime model selects the market state, while a regime-specific generator produces returns for studying market dynamics and risk measurement.

Develops quantum algorithms for tracing the Lasso regularisation path, building on least-angle regression. The paper analyses conditional speedups, robustness to approximate computations, a dequantised counterpart, and lower bounds. The speedups depend on the stated data-access and distributional assumptions.

Uses machine learning to connect molecular structures with surface-enhanced Raman scattering spectra. The paper studies two-way prediction between structures and spectra, including molecules outside the training set.

Develops a reinforcement-learning framework for subgame-perfect equilibrium in time-inconsistent decision problems. Extended backward policy iteration addresses the loss of standard dynamic-programming relationships, with sample-based algorithms illustrated through mean-variance portfolio selection.

Studies transformer-based generative models for financial time-series simulation under continuous conditions. The paper considers conditional scenario generation for financial data.

Builds a nanoparticle structural representation using data augmentation and machine learning. The work links extinction spectra with a mixture's purity, particle size and shape, considering prediction in both directions.

Examines stochastic differential games in which time inconsistency leads to nonlocal and nonlinear mathematical structures. The paper connects equilibrium decision problems with the analysis of the associated differential equations.

Studies conditional time-series generative adversarial networks for simulating asset prices. The focus is on generating financial trajectories while incorporating conditioning information.

Examines the difficulty of global optimisation when variance-based objectives introduce time inconsistency. The paper considers the implications for learning and sequential decision-making.

Studies portfolio optimisation using autoregressive deep reinforcement learning and learned intrinsic rewards. The work considers how the learning architecture and reward design shape investment decisions.

Studies robust equilibrium controls when the covariance matrix is ambiguous. An extended McKean-Vlasov dynamic-programming perspective connects the control problem, distribution-dependent dynamics and time-inconsistent objectives.

Studies data-driven portfolio optimisation with conditional value-at-risk and distributional uncertainty. A regime-switching ambiguity set allows the uncertainty description to reflect different market environments.

Studies nonlocal, fully nonlinear parabolic differential equations motivated by time-inconsistent control problems. The focus is on the mathematical structure needed to characterise equilibrium rather than standard dynamically optimal decisions.

Studies multi-period portfolio selection with transaction costs and long-only constraints. The paper examines how implementable investment decisions interact with time consistency in portfolio efficiency.

Connects Bayesian estimation with sequential portfolio optimisation and regularisation. The work considers how learning from financial data can be integrated with repeated investment decisions rather than treated as a separate preliminary step.

Studies social-distancing decisions by jointly considering economic activity and public-health consequences. The paper brings optimisation methods to the trade-offs involved in pandemic responses.

Studies a trading framework with a cumulative-prospect-theory actor and truncated quantile critics. The approach connects behavioural preferences with distributional elements of deep reinforcement learning.

Revisits policy iteration for decision objectives that are time-inconsistent. The paper connects reinforcement learning with equilibrium-based planning, where preferences over future actions can change as time passes.

Studies robust control over an infinite horizon with both continuous interventions and discrete impulses. The framework addresses decision-making when the model itself is uncertain and actions can take different forms.

Surveys machine-learning methods built on persistent homology and compares their use in learning tasks. The focus is on how topological information can be represented and incorporated into statistical prediction.

Studies linear-quadratic stochastic control with time-inconsistent preferences and uncertainty in the drift. The work brings model robustness and equilibrium decision-making into the same control setting.

Combines plasmonic feature construction with machine learning to connect nanoparticle properties and optical responses. The paper studies prediction of particle sizes and size distributions in a bidirectional setting.

Studies a two-stage supervised-learning approach to systemic financial risk measurement. Machine-learning components are used to represent the relationships relevant to measuring risk across a financial system.

Studies dynamic mean-variance portfolio selection in the presence of proportional transaction costs and a no-shorting constraint. The investment problem explicitly accounts for trading frictions and feasible portfolio positions.

Combines natural-language processing and Bayesian methods for stock-movement prediction. Social sentiment and interaction data provide information alongside the financial prediction task.

Studies robust mean-variance investment decisions when ambiguity aversion and risk aversion depend on the state. A closed-loop perspective connects these preferences with portfolio decisions as the market evolves.

Uses sparse learning in portfolio selection guided by relative volatility. The paper connects high-dimensional estimation and investment design when a parsimonious portfolio representation is desirable.

Studies portfolio construction using range-based measures of risk. The emphasis is on connecting risk estimation with a cost-conscious approach to investment decisions.

Studies expected-utility maximisation under a G-expectation formulation with ambiguous equicorrelation. The work considers investment decisions when dependence between assets is uncertain.

Develops a self-calibrated, regularised direct-estimation approach for high-dimensional statistical problems. Graphical selection and discriminant analysis provide two settings for studying the estimator.

Applies weighted persistent homology and machine learning to RNA flexibility analysis. Topological representations provide a way to connect molecular structure with a prediction task.

Studies robust, time-consistent mean-variance portfolio choice with multivariate stochastic volatility. The work combines evolving volatility, model uncertainty and dynamically consistent investment decisions.

Uses generative adversarial networks in a financial thought-experiment approach to robust portfolio selection. The paper connects synthetic financial scenarios with investment decisions in a high-dimensional setting.

Develops bootstrap-based KPSS testing for functional time series. The paper studies the validity and finite-sample behaviour of stationarity testing when each observation is a curve rather than a scalar.

Formulates sparse, high-dimensional multi-period portfolio selection through linear programming. The work links estimation and optimisation when the number of investable assets is large relative to the available data.

Studies time-consistent mean-variance investment when only risky assets are available. The paper examines portfolio decisions without using a risk-free asset as part of the investment opportunity set.

Studies stochastic control problems that combine model uncertainty with time-inconsistent preferences. The work addresses equilibrium decision-making when ordinary dynamic-programming arguments no longer apply directly.

Studies challenges arising in high-dimensional continuous-time mean-variance portfolio selection. The paper considers how statistical estimation issues affect an investment problem with many assets.

Examines degeneracy in Merton's portfolio-selection problem. The work focuses on the mathematical structure of the investment problem when standard non-degeneracy conditions fail.

Studies portfolio optimisation with stochastic volatility and uncertain asset correlation. The paper considers how uncertainty about dependence interacts with volatility dynamics in investment decisions.

Studies non-zero-sum reinsurance games with ambiguous correlations. The framework considers strategic insurance decisions when the dependence structure of the underlying risks is not known precisely.

Studies a robust, non-zero-sum stochastic differential game for reinsurance. The paper combines strategic interaction with uncertainty about the model governing insurance risks.

Studies investment and reinsurance decisions under model uncertainty and multiscale stochastic volatility. The work connects insurance risk management with financial-market dynamics evolving at different time scales.

Studies variance swaps in a model incorporating mean reversion, multiple stochastic-volatility factors and jumps. The paper considers how these features enter the valuation of volatility-linked contracts.

Studies asymptotic methods for American option valuation under a constant-elasticity-of-variance model. The work focuses on early exercise in a setting where volatility depends on the underlying asset price.