Publications

This technical note provides the complete mathematical proofs for the Causality-Bounded Pricing Theorem (CBPT), relativistic Itô lemma, maximum causal arbitrage distance (Dmax), and supporting models in RAP.

We derive the hyperbolic SPDE for price dynamics, establish martingale properties under causal filtrations, and prove no-arbitrage within light-cone domains. Numerical implementations in Python (with optimisations for runtime and memory) validate the theorems across scales, from Earth-Moon (0.2% premia) to Proxima Centauri (1499.8% premia). Empirical calibration uses DSN data for Mars (7.8% to 62.5% premia).

Code is illustrative and scalable, with potential for GPU acceleration to enable real-time commercial applications.

This paper introduces Relativistic Asset Pricing (RAP) — a framework for financial markets constrained by the finite speed of information. Where classical models assume instantaneous diffusion, RAP imposes an information-velocity limit, defining causal domains analogous to light cones in spacetime.

A Causality-Bounded Pricing Theorem (CBPT) is presented, establishing no-arbitrage conditions under causal filtrations. A relativistic Itô lemma is derived for delayed stochastic processes, and the maximum causal arbitrage distance is obtained, incorporating both deterministic and stochastic latency effects.

The model reconciles network physics and financial efficiency: as information speed approaches infinity, it converges to classical finance, while finite speeds capture real-world latency-bound arbitrage.

Capital markets are built on synchronized clocks. This paper extends financial market theory into regimes where communication delays become economically significant, demonstrating that standard financial models implicitly assume instantaneous information transmission — an assumption that fails when markets are separated by significant delays.

We formalise how relativistic causality constraints create distinct market regimes where traditional no-arbitrage conditions cannot hold, propose institutional mechanisms including temporal coordination systems suited to distributed economies, and outline an empirical research agenda for testing the framework’s implications.

This framework applies immediately to submarine cable finance, satellite communication markets, and disaster-disrupted economies, while establishing foundations for the emerging cislunar economy and eventual interplanetary commerce.