Financial mathematics student. I work on stochastic control, and within it on portfolio choice when the model's parameters are not known. This site keeps my projects, each labelled with its real status and with what I did by hand.
The mathematics of prices, risk and decisions under uncertainty: stochastic calculus, asset pricing, and the statistics needed to fit any of it to data.
Within that, the problem of acting optimally over time when the state evolves randomly: the Merton problem, the HJB equation, and the robust versions where the model itself is uncertain.
Within that, one question I keep returning to: the expected return is the input that matters most and the one the data pin down least. What does "optimal" mean once you take that seriously? I look at it from the data side (estimation error amplified by optimisation) and from the control side (drift uncertainty turns sup into sup–inf, and a no-trade region appears).
Everything quantitative is written in three underlying languages. I am trying to become fluent in all three, and I keep an honest record here of where each one stands.
The language things are proved in. Analysis, probability, stochastic processes, optimisation. The strongest of the three for me, and the one I lean on when the other two run out.
Now: stochastic processes, PDE and linear models at Berkeley; the Merton derivation by hand.
The language questions are asked in. Asset pricing, portfolio theory, market microstructure, and the vocabulary of actual markets, which textbooks skip.
Now: asset pricing coursework; a stock-selection paper from a CSI 300 competition; a first quantitative internship in 2027.
The language answers are produced in. Python for data and backtests, the discipline of reproducible experiments, eventually C++. The weakest of the three today, and the one I am working on hardest.
Now: writing the code myself instead of only reading it; verification scripts for both papers.
Finishing the semester at Berkeley. Back in Shanghai from January 2027 for a first quantitative internship, then a semester of research in financial mathematics at ShanghaiTech.