Consulting
Rigorous model audits, PDE system design, real options analysis, and MFG engagements for quantitative investment firms, energy companies, financial institutions, and corporate strategy teams.
Consulting Services
Model Audit
Independent review of existing quantitative models. We examine assumptions, numerical stability, calibration soundness, and convergence properties. Deliverable: written audit report with findings and recommended corrections.
PDE System Design
End-to-end design and prototyping of PDE-based pricing or control systems. HJB equations, Fokker–Planck systems, free-boundary problems. From mathematical formulation to production-ready numerical scheme.
MFG Engagement
Mean field game modelling for large-population strategic problems. Heterogeneous-agent equilibria, Nash conditions, and numerical solution of coupled HJB–Fokker–Planck systems. Applications in optimal execution, commodity market coordination, competitive market entry, and interbank dynamics.
Real Options Analysis
Optimal timing of capital investment, resource development, and market entry under uncertainty. HJB and free-boundary formulations of irreversible investment problems, real option valuation beyond standard approximations. Applications in energy project finance, corporate expansion decisions, and private equity portfolio strategy.
Who We Work With
Quantitative Hedge Funds & Prop Desks
Model audits for PDE-based pricing systems, HJB frameworks for optimal execution and position management, Hawkes process calibration for high-frequency dynamics, MFG equilibrium models for strategic order submission.
Algorithmic Trading & Market Design
Optimal execution via HJB and stochastic control, MFG models for strategic order submission in limit order books, Hawkes process calibration for order flow dynamics, and SPDE-based order book modelling. Applications in execution algorithm design, market maker strategy, exchange microstructure analysis, and the mathematical foundations of high-frequency trading systems.
Investment Banks & Structured Finance
PDE system design for exotic derivatives pricing, XVA and counterparty credit risk frameworks, credit derivative valuation under Markov migration models, bespoke numerical schemes for structured products.
High-Dimensional Modelling & Scientific AI
Optimal control and HJB equations in 50–200 state dimensions solved via physics-informed neural networks (PINNs), the deep Galerkin method, and neural operators — implemented in PyTorch, TensorFlow, and DeepXDE. Applications in multi-asset derivatives pricing, high-dimensional portfolio optimisation, systemic risk with large agent populations, and energy transition planning under many interacting state variables.
Corporate Strategy & Private Equity
Real options analysis for acquisition, expansion, and exit decisions. Dynamic investment timing under competitive uncertainty. Quantitative frameworks for strategic decisions that standard DCF methods cannot adequately capture.
Energy & Commodity Companies
Real options valuation for field development and infrastructure investment, optimal extraction under stochastic price dynamics, commodity storage and transportation optionality, bespoke energy price model design.
Engagement Process
-
01
Written Enquiry
Submit a written description of your problem, scope, and constraints. Be as detailed as possible — the precision of your brief determines the quality of our assessment. Strictly confidential. No NDA required at this stage. We respond in writing within three business days.
-
02
Proposal
Based on your written brief, we issue a formal written proposal: scope of work, methodology, deliverables, timeline, and a fixed project fee. The engagement begins only once the proposal is accepted in writing.
-
03
Engagement
Research and modelling conducted under a signed NDA. All communication is written. Progress updates are issued at agreed intervals. No change to scope proceeds without written approval.
-
04
Delivery
Final report and code (if applicable) delivered securely in writing. A written post-delivery review period is included for clarification questions.
Project-based pricing
All engagements are scoped and priced per project. Pricing reflects the complexity and duration of the work, not the number of hours logged. Retainer arrangements are available for clients with recurring research and advisory needs.
Submit a Written Enquiry
Describe your problem, scope, and constraints in writing. Be as detailed as possible — the precision of your brief determines the quality of our assessment. We respond in writing within three business days.