arXiv subjects

Hamza Virk

Publications and source records attributed to Hamza Virk.

4 recordsLinked to original sources

arXiv2026

The Spectral Structure of Latent Treatment Effects

Identifying heterogeneous treatment effects under unobserved confounding is central in observational causal inference. In proxy models with a discrete latent confounder, prior Synthetic Potential Outcomes (SPO) [Mazaheri-Squires-Uhler '25] recover the mixture of treatment effects through recursively constructed scalar moments. We show that this sequence is one projection of a more fundamental object. Under the same population factorization assumptions, there is an exact compressed observable operator: after projecting onto the shared proxy signal subspace, the difference of two treatment-arm quotient operators is similar to the diagonal matrix of latent treatment effects. Its eigenvalues are the latent effects; its lifted left eigenvectors, after anchor normalization, recover the target-proxy feature matrix and then the latent mixture proportions. Every scalar SPO moment is a bilinear functional of a power of this operator. The resulting estimator handles overcomplete proxy systems, replaces high-order scalar inversion with finite-dimensional spectral analysis, and admits high-probability first-order perturbation bounds for treatment effects, feature rows, and simplex-projected mixture weights.

cs.LG↗

arXiv2025

Arbitrage-Free Pricing with Diffusion-Dependent Jumps

Standard jump-diffusion models assume independence between jumps and diffusion components. We develop a multi-type jump-diffusion model where jump occurrence and magnitude depend on contemporaneous diffusion movements. Unlike previous one-sided models that create arbitrage opportunities, our framework includes upward and downward jumps triggered by both large upward and large downward diffusion increments. We derive the explicit no-arbitrage condition linking the physical drift to model parameters and market risk premia by constructing an Equivalent Martingale Measure using Girsanov's theorem and a normalized Esscher transform. This condition provides a rigorous foundation for arbitrage-free pricing in models with diffusion-dependent jumps.

q-fin.MF↗

arXiv2025

Entry deterrence and antibiotic conservation under post-entry Bertrand competition

We analyze how an incumbent antibiotic monopolist responds to the threat of post-entry Bertrand competition by a vertically differentiated rival. In a two-period model where current production drives future resistance, Bertrand competition leads to a winner-take-all outcome. We find that strategic deterrence is optimal regardless of bacterial cross-resistance to prospective rival drugs. In contrast with post-entry Cournot competition, anticipated price competition provides the incumbent with a stronger strategic incentive for conservation.

econ.GN↗

arXiv2025

Blind Inverse Game Theory: Jointly Decoding Rewards and Rationality in Entropy-Regularized Competitive Games

Inverse Game Theory (IGT) methods based on the entropy-regularized Quantal Response Equilibrium (QRE) offer a tractable approach for competitive settings, but critically assume the agents' rationality parameter (temperature $\tau$) is known a priori. When $\tau$ is unknown, a fundamental scale ambiguity emerges that couples $\tau$ with the reward parameters ($\theta$), making them statistically unidentifiable. We introduce Blind-IGT, the first statistical framework to jointly recover both $\theta$ and $\tau$ from observed behavior. We analyze this bilinear inverse problem and establish necessary and sufficient conditions for unique identification by introducing a normalization constraint that resolves the scale ambiguity. We propose an efficient Normalized Least Squares (NLS) estimator and prove it achieves the optimal $\mathcal{O}(N^{-1/2})$ convergence rate for joint parameter recovery. When strong identifiability conditions fail, we provide partial identification guarantees through confidence set construction. We extend our framework to Markov games and demonstrate optimal convergence rates with strong empirical performance even when transition dynamics are unknown.

cs.LG↗