Autospeculation: Endogenous Speculative Dynamics

• Autospeculation is the phenomenon where self-generated forecasts or actions alter the environment, creating recursive feedback that impacts asset prices, AI outputs, or institutional dynamics.
• It is explored across financial models with power-law returns, agent-based markets replicating stylized patterns, and macroeconomic systems where speculative behavior influences growth and policy outcomes.
• In computational systems and autonomous agents, autospeculation drives accelerated processing and adaptive strategies by leveraging internal predictions, enabling pre-execution and speculative computation.

Searching arXiv for papers on autospeculation and related usages. Autospeculation denotes self-generated speculative dynamics in which forecasting, bidding, or pre-executing a future state changes the environment in a way that can partially validate the original conjecture. The recent literature suggests a polysemous term. In financial theory, it names endogenous feedback loops in which expected price changes induce trades that move prices in the expected direction, or governance mechanisms whose own redemption rules manufacture speculative incentives (Inoua, 2016, Inoua et al., 2023, Eschenbaum et al., 27 May 2025). In autonomous-agent research, it refers to AI systems whose forecasts or liquidation strategies generate bubbles, busts, or adaptive instability in simulated asset markets (Saxena et al., 9 Apr 2026, Hymas et al., 6 Feb 2026). In machine-learning systems, it denotes self-speculative computation, where a model or workflow speculates about its own future outputs rather than relying on an external draft model (Hu et al., 6 May 2025, Anari et al., 11 Nov 2025, Fareed, 5 Jun 2026).

1. Endogenous speculative feedback in financial theory

A core formalization treats speculation as a feedback mechanism: traders buy when they expect price rises and sell when they expect price falls, and that very order flow pushes prices in the anticipated direction. In "Speculation and Power Law" the basic assumptions are

$x_{it}=\alpha r_{it}^e,\qquad r_t=\beta x_t,$

so aggregate returns satisfy

$r_t=a_t \bar r_t^e,\qquad a_t=\alpha\beta N_t.$

Under passive expectations,

$\bar r_t^e=r_{t-1}+\bar\varepsilon_t,$

the return process becomes

$r_t=a_t r_{t-1}+e_t,$

a random-coefficient autoregression whose stationary tail exponent is characterized by

$\mathbb{E}(a^\mu)=1.$

The paper identifies this endogenous amplification, rather than exogenous fat-tailed news, as the source of power-law returns (Inoua, 2016).

A related but broader classical formulation embeds speculative feedback into a market with reservation returns, excess demand, and adaptive expectations. In "A Classical Model of Speculative Asset Price Dynamics" returns satisfy

$$r_t = n_t^I r_t^e + n_t^{II}\frac{v_t^e-p_t}{p_t} - \gamma,$$

and in the pure speculative case

$$r_t = n_t^I r_{t-1} + m_t \varepsilon_t\,\text{news}_t - \gamma.$$

The paper attributes excess volatility, fat tails, clustered volatility, and persistent bubbles to this internal expectation–trading loop, and states that bubble size increases with the proportion of speculators and decreases with the trading horizon (Inoua et al., 2023).

Not all formal models imply that autospeculation is necessarily upward-biased. "Shorting in Speculative Markets" shows that once heterogeneous-belief traders face quadratic costs-of-carry and can short, speculation contains several opposed options: a resale option for longs, a delay option for longs, and a repurchase option for shorts. The equilibrium price solves a Hamilton–Jacobi–Bellman equation of the form

$$\partial_t v(t,x) + \sup_{I\subseteq \{1,\dots,n\}} \Big(\mu_I\partial_x v + \tfrac12 \operatorname{tr}(\Sigma_I^2\partial_{xx}v)-\kappa_I\Big)=0,$$

and the paper shows that dynamic speculative price can be above or below the static buy-and-hold benchmark. This suggests that autospeculation is better understood as endogenous dynamic feedback than as a synonym for overpricing (Nutz et al., 2017).

2. Agent-based speculative ecologies and stylized facts

In agent-based market models, autospeculation is represented as an ecology of rule-driven traders who adapt on the basis of realized or cognitively perceived gains. "Development of an agent-based speculation game for higher reproducibility of financial stylized facts" defines a repeated market with $N$ players, memory length $M$, $r_t=a_t \bar r_t^e,\qquad a_t=\alpha\beta N_t.$0 strategies per player, board-lot amount $r_t=a_t \bar r_t^e,\qquad a_t=\alpha\beta N_t.$1, and cognitive threshold $r_t=a_t \bar r_t^e,\qquad a_t=\alpha\beta N_t.$2. The baseline simulations use

$r_t=a_t \bar r_t^e,\qquad a_t=\alpha\beta N_t.$3

Order size is wealth-scaled,

$r_t=a_t \bar r_t^e,\qquad a_t=\alpha\beta N_t.$4

price change follows

$r_t=a_t \bar r_t^e,\qquad a_t=\alpha\beta N_t.$5

and strategies are evaluated in a cognitive world with

$r_t=a_t \bar r_t^e,\qquad a_t=\alpha\beta N_t.$6

The model reproduces 10 of the 11 stylized facts listed by the authors under a single parameter setting; the only one not reproduced is gain/loss asymmetry (Katahira et al., 2019).

The extension in "An extended Speculation Game for the recovery of Hurst exponent of financial time series" modifies the price-change rule to

$r_t=a_t \bar r_t^e,\qquad a_t=\alpha\beta N_t.$7

where the perturbative term stands in for effects beyond pure speculative behavior. The paper reports that the original model yields $r_t=a_t \bar r_t^e,\qquad a_t=\alpha\beta N_t.$8 with $r_t=a_t \bar r_t^e,\qquad a_t=\alpha\beta N_t.$9, whereas with moderate perturbation, exemplified by $\bar r_t^e=r_{t-1}+\bar\varepsilon_t,$0, the Hurst exponent rises to $\bar r_t^e=r_{t-1}+\bar\varepsilon_t,$1 with $\bar r_t^e=r_{t-1}+\bar\varepsilon_t,$2. It also states a tradeoff: as perturbation grows, return distributions become less heavy-tailed and other stylized features weaken. A plausible implication is that pure speculative feedback can generate many short-horizon regularities while underproducing long-horizon wandering unless additional order-flow sources are introduced (Katahira et al., 2019).

These agent-based constructions differ from the Kesten-style analytical models in one important respect. They make round-trip trading, variable holding periods, inactivity, and wealth-dependent sizing explicit. That move preserves the idea of autospeculation as endogenous feedback, but relocates it from a reduced-form return recursion to a heterogeneous trading ecology.

3. Macroeconomic and institutional forms of autospeculation

At macroeconomic scale, autospeculation can arise when speculative finance is itself an endogenous function of nominal growth. "Inflation and speculation in a dynamic macroeconomic model" augments the Keen debt-cycle framework with a speculative flow $\bar r_t^e=r_{t-1}+\bar\varepsilon_t,$3, normalized as

$\bar r_t^e=r_{t-1}+\bar\varepsilon_t,$4

and obtains the four-dimensional system

$\bar r_t^e=r_{t-1}+\bar\varepsilon_t,$5

$\bar r_t^e=r_{t-1}+\bar\varepsilon_t,$6

$\bar r_t^e=r_{t-1}+\bar\varepsilon_t,$7

$\bar r_t^e=r_{t-1}+\bar\varepsilon_t,$8

Here speculation responds to nominal growth $\bar r_t^e=r_{t-1}+\bar\varepsilon_t,$9, raises debt accumulation, compresses profit share through interest burdens, and can generate repeated financial crises as a natural pace of the economy. The paper emphasizes that adding speculation can turn a previously inflationary good equilibrium into a deflationary one (Grasselli et al., 2014).

In institutional design, autospeculation can be manufactured directly by governance-and-exit rules. "Repeated Auctions with Speculators: Arbitrage Incentives and Forks in DAOs" studies a DAO that repeatedly auctions governance shares while allowing redemptive exit if speculators accumulate enough shares to trigger a fork. The speculator’s valuation is the expected discounted redemption value

$r_t=a_t r_{t-1}+e_t,$0

and the paper derives an interior optimal bid

$r_t=a_t r_{t-1}+e_t,$1

Because

$r_t=a_t r_{t-1}+e_t,$2

can hold, the bid can exceed raw redemption value: bidding itself raises expected auction prices, treasury size, and hence future redemption value. The paper classifies equilibria into Type I, where exploitative exit is guaranteed; Type II, where it occurs only in expectation; and Type III, where it never occurs. Under its fourth redemption mechanism,

$r_t=a_t r_{t-1}+e_t,$3

it proves that no Type I or Type II equilibrium can arise and no forking occurs (Eschenbaum et al., 27 May 2025).

These two literatures use different state variables and institutions, but both locate autospeculation in a recursive mechanism: current financial choices alter the state that determines the future value of those same choices.

4. Autonomous AI agents and machine-generated speculation

In simulated asset markets with LLMs, autospeculation becomes an empirical behavioral property of autonomous forecasters. "Machine Spirits: Speculation and Adaptation of LLM Agents in Asset Markets" studies 15 LLMs in a positive-feedback pricing environment with $r_t=a_t r_{t-1}+e_t,$4 agents over $r_t=a_t r_{t-1}+e_t,$5 periods and fundamental value

$r_t=a_t r_{t-1}+e_t,$6

Prices are determined by average one-step-ahead forecasts,

$r_t=a_t r_{t-1}+e_t,$7

A run is classified as a bubble if price exceeds 300 for at least 3 consecutive periods. The paper reports that some models generate strong bubbles in homogeneous populations, while frontier models that are fundamentalist in isolation can nevertheless adapt in mixed markets. In the six-model mixed market, despite only two of six models being naturally bubble-forming, the market bubbles roughly 50% of the time. The authors describe these systematic deviations from rational expectations as “machine spirits” (Saxena et al., 9 Apr 2026).

The paper’s adaptive results sharpen the notion of autospeculation. Advanced models do not simply fail to stabilize; some strategically shift toward trend-following when that improves forecast-accuracy earnings. This suggests that autospeculation can be intrinsic to a model class, emergent from heterogeneous AI ecologies, or induced by payoff-driven adaptation.

A more radical intervention appears in "Quenching Speculation in Quantum Markets via Entangled Neural Traders". There, 8 reinforcement-learning traders begin with 10 cash units and 10 stock units each, and their valuations are quantum-mediated. Entanglement is introduced by

$r_t=a_t r_{t-1}+e_t,$8

and adjusted valuations are extracted from

$r_t=a_t r_{t-1}+e_t,$9

The paper reports that the classical market rapidly converges to liquidation strategies that collapse the asset value, whereas the quantum-correlated market stabilizes prices and increases net worth. In its quantized $\mathbb{E}(a^\mu)=1.$0-guessing game, phase-mismatched maximal entanglement removes the pathological pure-strategy Nash equilibrium that drives collapse in the classical game, while mixed equilibria remain non-degenerate (Hymas et al., 6 Feb 2026).

5. Autospeculation as self-speculative computation

A distinct computational meaning has emerged in generative modeling and systems. In "Diffusion Models are Secretly Exchangeable: Parallelizing DDPMs via Autospeculation", autospeculation means that a diffusion model uses its own current prediction as a proposal for several future denoising steps. Under a stochastic-localization reparameterization, equal-length increments are exchangeable, which enables Autospeculative Decoding (ASD). The method preserves the exact law of the discretized process and yields expected parallel complexity

$\mathbb{E}(a^\mu)=1.$1

corresponding to a $\mathbb{E}(a^\mu)=1.$2 parallel speedup over $\mathbb{E}(a^\mu)=1.$3 sequential steps. The paper reports wall-clock speedups of roughly $\mathbb{E}(a^\mu)=1.$4 to $\mathbb{E}(a^\mu)=1.$5 across image and robot-diffusion settings, without measurable quality loss (Hu et al., 6 May 2025).

"Parallel Sampling via Autospeculation" generalizes the same idea. It introduces speculative rejection sampling, where the speculative distribution $\mathbb{E}(a^\mu)=1.$6 is built from the same oracle that defines the target distribution $\mathbb{E}(a^\mu)=1.$7, rather than from a separate draft model. In any-order autoregressive sampling it gives an exact sampler with expected

$\mathbb{E}(a^\mu)=1.$8

rounds, and in diffusion it gives an expected

$\mathbb{E}(a^\mu)=1.$9

parallel-round algorithm for sampling $$r_t = n_t^I r_t^e + n_t^{II}\frac{v_t^e-p_t}{p_t} - \gamma,$$0-close to $$r_t = n_t^I r_t^e + n_t^{II}\frac{v_t^e-p_t}{p_t} - \gamma,$$1 under bounded support. Here autospeculation is sequence-level rather than token-level: entire blocks are proposed and verified at once (Anari et al., 11 Nov 2025).

A systems version appears in "Cost-Aware Speculative Execution for LLM-Agent Workflows". There, autospeculation means launching a downstream operation before its upstream dependency completes, using a predicted input $$r_t = n_t^I r_t^e + n_t^{II}\frac{v_t^e-p_t}{p_t} - \gamma,$$2. The decision rule prices speculation in dollars: $$r_t = n_t^I r_t^e + n_t^{II}\frac{v_t^e-p_t}{p_t} - \gamma,$$3

$$r_t = n_t^I r_t^e + n_t^{II}\frac{v_t^e-p_t}{p_t} - \gamma,$$4

$$r_t = n_t^I r_t^e + n_t^{II}\frac{v_t^e-p_t}{p_t} - \gamma,$$5

The paper restricts speculation to admissible edges that are side-effect-free, idempotent, or stageable behind a commit barrier, and estimates success probability with a Beta-Binomial posterior keyed to dependency type (Fareed, 5 Jun 2026).

This computational literature uses “autospeculation” in a non-financial sense, but the structural analogy is close: present actions are taken on the basis of a predicted future state that is partially endogenous to the same system.

6. Terminological scope, misconceptions, and source limits

The term should not be conflated with several homonymous “AutoSpec” frameworks that address unrelated problems. "AutoSpec: Safety Rule Evolution for LLM Agents via Inductive Logic Programming" concerns rule-based safety refinement for agent traces, not speculative dynamics (Ma et al., 23 Jun 2026). "AutoSpec: An Agentic Framework for Automatically Drafting Patent Specification" concerns patent-specification drafting (Shea et al., 23 Sep 2025). "Automating the Refinement of Reinforcement Learning Specifications" concerns logical-specification refinement in SpectRL-based reinforcement learning (Ambadkar et al., 30 Nov 2025). These works share a name but not the concept of autospeculation.

A second misconception is that autospeculation always means price inflation or bubble formation. The financial literature is more precise. In the disagreement models with shorting and convex carrying costs, dynamic speculation can lower price relative to a static benchmark because delay and repurchase options counteract resale options (Nutz et al., 2017). In the quantum-market paper, the salient pathology is a speculative bust rather than a bubble (Hymas et al., 6 Feb 2026). In computational systems, the term does not refer to asset prices at all, but to self-proposed execution paths (Hu et al., 6 May 2025, Anari et al., 11 Nov 2025, Fareed, 5 Jun 2026).

A final caution concerns bibliographic noise. The arXiv listing "A simulated electronic market with speculative behaviour and bubble formation" (Cofre et al., 2023) is described in the supplied details as a blank Elsevier manuscript template with placeholder text and no substantive model, experiments, equations, figures, or results. It therefore does not support technical claims about electronic markets, order books, or bubble dynamics.

Taken together, the literature suggests that autospeculation is best treated not as a single doctrine but as a family resemblance concept. Its common core is recursive endogeneity: an agent, market, or model takes action on the basis of a forecast, proposal, or exit value that is itself altered by that action.