This paper introduces a signature-based framework for optimal execution in statistical arbitrage with path-dependent signals, unifying alpha generation and execution within a single truncated signature state. A central quadratic reduction theorem shows that, when trading speeds are restricted to signature-linear controls, the path-dependent execution problem becomes a finite-dimensional concave quadratic program that can be solved off-line; live execution then reduces to a single matrix-vector multiplication. The approach is demonstrated on synthetic mean-reverting log-spread dynamics and on a historical equity-pairs workflow (Shell–BP), where the learned policy outperforms a standard z-score benchmark on accounting metrics such as return on turnover [page::4][page::7][page::10]. The framework also connects with classical Almgren–Chriss/LQ setups and provides a principled route to incorporate temporary impact, inventory risk, and dollar-neutrality within a single optimisation [page::4].
Heavy-tailed extensions of denoising diffusion models replace the Gaussian noise by a Gaussian variance mixture εi = Ai zi: denoising Lévy probabilistic models (DLPM) take the mixing variables Ai i.i.d. across coordinates, Student-t EDM takes a single A shared by all coordinates. [page::0]
Neither extreme has dynamics, yet temporal dependence of the noise amplitude— volatility clustering—is the defining stylized fact of the financial data these models target. [page::0]
We introduce the Denoising Subordinated Probabilistic Model (DSPM), whose mixing vector is a stationary AR(1) chain driven by tempered-stable subordinator increments—the discretetime Barndorff-Nielsen–Shephard stochastic volatility process—running along the data axis. [page::0]
Conditionally on the chain, the entire DDPM machinery survives verbatim, and we prove closed-form identities linking the chain parameters to the excess kurtosis and the squarednoise autocorrelation, yielding an exactly identified, analytically invertible calibration with a falsifiable feasibility bound ρr2(1) < K/(3(K + 2)). [page::0]
DDPM, DLPM-type stable noise, and shared-scale Student-t-type noise are boundary cases of one memory parameter. [page::0]
We then prove a result that delimits the entire design space: if the denoiser is conditioned on A (as sufficiency demands), the mixing law is a nuisance—in the exact-denoiser limit the generated distribution is invariant to it, and interventions on A have no effect. [page::0]
Controlled experiments (identical denoiser, schedule, budget; only the law of A or the conditioning bit varies) confirm both halves: conditioned models match the data’s clustering regardless of the mixing law, and a designed 8 volatility shock moves the generated amplitude envelope by less than 13% against a naive prediction of +183%; blind models transmit the noise structure exactly as calibrated—lag-one squared-return autocorrelation 0.151 against the calibrated 0.161 with the predicted geometric decay, while the i.i.d. variant’s clustering collapses to 0.008. [page::0]
The mixing law controls what structure the noise offers; the conditioning bit controls whether it transmits. [page::0]
Finally we close the loop (v2): coupling the chain to the data through a variational volatility encoder (with a log-normal volatility prior, for closed-form KL) restores control—provided the objective retains the stochastic-volatility likelihood whose log-determinant term the simplified denoising loss discards; naive β-weighted couplings collapse or leak, and both failure modes are documented. [page::0]
With it, the same 8 intervention scales the envelope by 3.07 (naive scaling: 2.83), the encoder tracks the true latent volatility of held-out paths (per-path correlation 0.57; 0.76 pooled), and the learned prior memory moves from its moment-calibrated initialization toward the true persistence. [page::0]
The cost is substantial and stated plainly: the coupled model’s unconditional kurtosis falls below even the Gaussian baseline—fidelity and control are demonstrated separately, not yet jointly. [page::0]
The paper develops a portfolio-level framework to model cloud interruption and measure diversification in cyber insurance, distinguishing standard and systemic regimes, and proposing an optimization to balance profitability with resilience to accumulation shocks. It formalizes a loss timeline, derives macro-level risk measures (mean, VaR, CTE) under Gaussian asymptotics, and provides underwriting guidelines to reduce exposure to cloud-outage scenarios. A numerical illustration with five providers shows how aggregate exposures should be allocated to maintain mutualization in ordinary conditions while limiting concentration under stress [page::0][page::4].