My work spans several interconnected areas of applied mathematics and quantitative finance. The common thread is the rigorous analysis of mathematical models — their structure, numerical treatment, and application to real problems in finance and stochastic systems. Click any area below to browse entries.
Market Modeling
Stochastic volatility models, limit order book dynamics, price impact, and the statistical properties of high-frequency trade arrivals. Includes calibration of Heston and SABR models and Hawkes process models for order flow.
Stochastic Optimal Control
Hamilton-Jacobi-Bellman equations, viscosity solutions, dynamic programming, and singular control. Applications include optimal execution, portfolio optimisation, and irreversible investment under uncertainty.
Stochastic Analysis
Malliavin calculus, backward stochastic differential equations, large deviations, and stochastic filtering. Theoretical foundations underpinning the rigorous treatment of randomness in continuous-time models.
Agent Based Modeling
Heterogeneous agent models of financial markets, emergent price dynamics, herding and contagion in financial networks, and synthetic market generation via calibrated multi-dimensional point processes.
Mean Field Games
Coupled Hamilton-Jacobi and Fokker-Planck PDE systems arising in large-population differential games. Topics include the master equation, common noise, McKean-Vlasov optimal control, and applications to systemic risk and interbank lending.
Mathematical Finance
Arbitrage theory, equivalent martingale measures, derivative pricing, term structure models, and coherent risk measures. Rigorous foundations connecting probability theory to the valuation and hedging of financial instruments.
Other
Notes on quantitative methods in algorithmic trading, risk measures, numerical linear algebra, and deep learning approaches to derivative pricing. Shorter pieces and surveys that do not fit neatly into the above categories.
