Supervision

I am not taking postdocs or students at this time for research supervision, nor am I hiring research assistants. I appreciate the interest, but due to the large volume of emails I receive with such requests, I am unfortunately unable to reply to most individual inquiries.

Research Interests

I have two primary research interests, both of which use deep learning for computation.

1. Computational methods in mathematical finance, particularly term structure modeling and pricing interest rate derivatives using continuous-time techniques and deep learning.
2. Computational macro-finance with a focus on general equilibrium policy analysis, where I study questions at the intersection of household finance, macroeconomics, and asset pricing.

Working Papers

Mathematical Finance

• Feynman-Kac Derivatives Pricing on the Full Forward Curve
  • This paper introduces a no-arbitrage, Monte Carlo-free approach to pricing path-dependent interest rate derivatives. The Heath-Jarrow-Morton model gives arbitrage-free contingent claims prices but is infinite-dimensional, making traditional numerical methods computationally prohibitive. To make the problem computationally tractable, I cast the stochastic pricing problem as a deterministic partial differential equation (PDE). Finance-Informed Neural Networks (FINNs) solve this PDE directly by minimizing violations of the differential equation and boundary condition, with automatic differentiation efficiently computing the exact derivatives needed to evaluate PDE terms. FINNs achieve pricing accuracy within 0.04 to 0.07 cents per dollar of contract value compared to Monte Carlo benchmarks. Once trained, FINNs price caplets in a few microseconds regardless of dimension, delivering speedups ranging from 300,000 to 4.5 million times faster than Monte Carlo simulation as the state space discretization of the forward curve grows from 10 to 150 nodes. The major Greeks—theta and curve deltas—come for free, computed automatically during PDE evaluation at zero marginal cost, whereas Monte Carlo requires complete re-simulation for each sensitivity. The framework generalizes naturally beyond caplets to other path-dependent derivatives—caps, swaptions, callable bonds—requiring only boundary condition modifications while retaining the same core PDE structure.

Macro-Finance and Policy Evaluation

• Real and Asset Pricing Effects of Employer Retirement Matching
  • This paper demonstrates that employer retirement matching increases firm investment and output through a novel general equilibrium mechanism: policies affecting household savings incentives alter the stochastic discount factor (SDF), thereby changing equilibrium asset prices and real investment. This insight extends to any intervention shifting household intertemporal marginal rates of substitution. I integrate stochastic overlapping generations with neoclassical q-theory, where matching enters households’ Euler equations and the household-implied SDF determines the firm’s cost of capital. Analytically, I prove that matching unambiguously increases the SDF, reduces equilibrium returns, and raises capital investment—households tolerate lower market returns because effective returns inclusive of the match remain attractive. Solving the full 60-period stochastic model using finance-informed neural networks confirms these predictions: empirically realistic matching reduces equity returns by 79 basis points, increases capital by 6.1\%, and raises wages by 1.7\%. These findings highlight the importance of general equilibrium analysis when evaluating policies affecting household portfolio choice.
• Student Debt (Forgiveness) in General Equilibrium
  • This paper evaluates the Biden Administration’s proposed student loan forgiveness policy in a stochastic overlapping generations model with 60 periods of life and three household types differentiated by student debt-to-income ratios. The central finding is that student loan forgiveness generates minimal real economic effects, contradicting the policy’s stated objective of promoting wealth accumulation among over-leveraged borrowers. Despite reduced debt burdens, borrowers allocate the transfer primarily toward consumption rather than retirement savings or productive investment, leaving aggregate capital, production, wages, and asset prices virtually unchanged. For non-borrowers, the policy delivers welfare losses driven almost entirely by higher tax obligations needed to finance the forgiveness, with negligible offsetting gains from general equilibrium spillovers. While forgiveness does provide a small welfare benefit through reduced consumption risk—acting as government-provided intergenerational risk sharing—this effect is quantitatively minor. The results suggest that student loan obligations were not the binding constraint on wealth accumulation for young highly leveraged borrowers, and the forgiveness program operates primarily as a fiscal transfer rather than a mechanism to unlock productive investment.
  • Presentations:
    • Society for the Advancement of Economic Theory (Santiago, Chile, 2024)
    • Society for Economic Measurement (Calgary, AB, 2022)

Open-Source Research Tool: Finance-Informed Neural Networks for Overlapping Generations Models

I developed a flexible computational framework for solving stochastic overlapping generations models using deep learning. The code implements policy iteration with neural networks that directly incorporate economic constraints (Euler equations, feasibility conditions) into the training process. This grid-free approach leverages GPU acceleration to efficiently solve high-dimensional complex dynamic stochastic general equilibrium models.

Designed with modularity in mind, the modular nature of the program allows researchers to easily adapt the methodology to their own models by customizing model parameters, constraints, and equilibrium conditions.

GitHub: Finance-Informed Neural Networks for OLG Models