Quant Finance PhD Track

Core: measure-theoretic probability, conditional expectation and martingales; solve proof-based exercises before continuous-time pricing.

Bayesian inference, computation and model checking.

Epistemology, induction and causation.

Discrete-time asset pricing and risk-neutral valuation.

Brownian motion, Ito calculus, martingales and continuous-time pricing.

Derivatives, Black-Scholes, Greeks, volatility and risk.

Pricing kernels, expected returns and portfolio theory.

Duality, constrained optimization and portfolio problems.

Decision-analysis course backbone: uncertainty, simulation, discounted cash flow and risk. Work through the published notes, assignments and quizzes.

Preference axioms; derive expected-utility representation for finite lotteries, certainty equivalents, risk aversion and Kelly growth. Work exercises on estimation error, drawdowns and fractional Kelly.

Falsifiability and the design of research tests.

Read the decision-theoretic chapters and solve exercises on utility, Bayesian updating and optimal decisions.

Graduate core: loss functions, risk, Bayes rules, minimaxity, admissibility and complete-class ideas. Derive results and solve proof-based exercises.

Calculate value of information; compare Bayes and minimax decisions; study sensitivity to priors, misspecified models, ambiguity and behavioral departures from expected utility.

Financial data sources, identifiers, governance and reliable ingestion-to-production pipelines.

Lectures and assignments.

Regression, classification, trees, regularization and validation.

Time series, econometrics and volatility modeling.

Neural networks, optimization and representation learning.

Attention, temporal shifts and leakage-resistant model validation.

Decision theory III: utility foundations, mixed strategies, minimax and zero-sum games. Prove finite-game results and solve equilibrium exercises; prioritize relevant chapters.

Multiple testing, false discovery, selection bias, shrinkage and uncertainty; dependent-data validation, leakage and nonstationarity. Derive error controls and critique empirical papers.

Autocorrelation, spectral analysis, filtering, state-space models, Kalman filters and hidden Markov models. Work derivations and inference exercises.

Entropy, KL divergence, mutual information, concentration, regularization and covariance estimation. Derive bounds and connect them to noisy prediction.

Dynamic programming, policy evaluation and control.

Work exercises and implement core algorithms.

Dynamic programming, HJB equations and execution costs.

Philosophy of mind, consciousness and metaphysics.

Read critically alongside philosophy of religion.

Logic, rationality, ethics, Christian theology, comparative religion, scientific spirituality and transhumanism.

Sequential tests, optimal stopping, Bellman equations, exploration/exploitation, stochastic bandits and regret bounds. Solve analytical problems before reading research extensions.

Online prediction, expert aggregation, adversarial regret and sequential investment. Derive core regret bounds; compare assumptions with financial data.

Optional refresher: skip the full course/module if you can solve its representative problems; revisit gaps when needed. Review as needed; solve problem sets.

Optional refresher: skip the full course/module if you can solve its representative problems; revisit gaps when needed. Proofs, limits, continuity and integration.

Optional refresher: skip the full course/module if you can solve its representative problems; revisit gaps when needed. Distributions, conditional expectation and limit theorems.

Optional refresher: skip the full course/module if you can solve its representative problems; revisit gaps when needed. Estimation, hypothesis testing and regression.

Optional refresher: skip the full course/module if you can solve its representative problems; revisit gaps when needed. ODEs, PDEs, numerical linear algebra and Monte Carlo; Python/C++ implementations.

Write proofs, worked exercises and reproducible numerical experiments.

Convergence tests, variance reduction and confidence intervals. Learn any missing numerical methods while building it.

Analytic and numerical pricing; Greeks and independent validation. Study the required PDE and numerical techniques alongside implementation.

Build the Deimos v2 automated betting and trading system.

Market-data pipelines, order simulation, slippage and transaction costs.

Walk-forward evaluation, baselines and reproducible results.

Compare against simple baselines under costs and risk constraints.

Automated execution, monitoring, reconciliation and risk limits.

Reproduce results, audit assumptions and document failures.

Literature review, scope, hypothesis and evaluation criteria.

Derivations, reproducible code, robustness checks and limitations.

State contributions clearly; seek independent critical feedback.

Connect the research question, theory, methods, evidence and conclusions.

Present the work, address external feedback and archive code, data and manuscript.