PORTFOLIO SELECTION UNDER RATIONAL INATTENTION WITH VARYING INTEREST RATES

WITH DANIEL CONUS (DEPARTMENT OF MATHEMATICS, LEHIGH UNIVERSITY)

We extend Huang and Liu’s (2007) rational inattention framework by introducing a stochastic interest rate to study how optimal signal precision affects portfolio choice and investor welfare. Relative to the constant-rate benchmark, a rationally inattentive investor can achieve higher expected terminal utility under interest-rate fluctuations when signal precision and portfolio allocation are jointly optimized. In this sense, the framework preserves the central logic of portfolio theory while extending it to a richer environment with information frictions and stochastic interest-rate uncertainty. Methodologically, the paper combines stochastic filtering for belief updating about latent states with continuous-time stochastic control and Hamilton--Jacobi--Bellman analysis to characterize the joint problem of information acquisition and portfolio choice. Replacing the constant rate in the benchmark model with a trend-based estimate also yields convergence in the value function, providing a useful benchmark for rationally inattentive agents facing uncertainty in both information acquisition and portfolio design.

A central implication of the model is the emergence of corner solutions in optimal attention allocation. This is not a problem: it arises naturally from concave utility and convex information cost, so that diminishing marginal benefit and rising marginal cost make concentration on a single unknown state optimal at a given moment. Economically, this is also intuitive, since attention is often directed to the signal with the highest marginal value relative to marginal cost rather than smoothly split across all sources. At the same time, this is fundamentally a point-in-time result tied to the Huang and Liu framework, where information flow is dynamic but signal precision is chosen only once at the initial date and then remains fixed over the investment horizon. Once signal precision is allowed to adjust over time, instantaneous corner choices may still arise, but their cumulative frequencies generate an effective time-averaged attention ratio over the full horizon, so that non-corner allocations can emerge at the intertemporal level. This observation in turn provides the foundation for my job market paper on dynamic signal precision.

DYNAMIC SIGNAL PRECISION IN RATIONALLY INATTENTIVE DECISION-MAKING (Job Market Paper)

WITH DANIEL CONUS (DEPARTMENT OF MATHEMATICS, LEHIGH UNIVERSITY)

This paper extends the rational inattention framework by shifting attention from information inflow alone to the dynamic structure of signal precision. We argue that an information environment, much like a fluid in physics, is characterized not only by its quantity, but also by its direction and density (precision); these dimensions jointly shape the rationality of decision-makers. While the Sims (2003) framework emphasizes information quantity under a capacity constraint, and later dynamic rational inattention models allow information to evolve over time, they typically focus on Shannon entropy or, even when they incorporate signal precision, treat it as a one-time choice made at the initial date. By contrast, we develop a continuous-time rational inattention portfolio model in which signal precision is endogenously adjusted over time in response to evolving uncertainty. The model generates a dynamic learning-decision-value loop and derives an additional dynamic effect in the value function through the intertemporal tradeoff between attention reward and attention cost.

This perspective is especially relevant in the AI era, where information is increasingly pushed, filtered, ranked, and fed to agents rather than simply sought out. Rationality is therefore shaped not only by how much information is available, but also by the structure of what is received. In this sense, one may say: you are what you eat, and you are what you are fed. The analysis establishes convergence toward the baseline precision regime, classifies transitional dynamics across low-, moderate-, and high-risk environments, and identifies six cases---degenerate adjustment, latent-risk monitoring, immediate rescue, routine monitoring, mild over-attention, and short-run correction. It further characterizes the duration of monitoring, correction, and rescue regimes before the system returns to the baseline regime. Information precision thus operates as a dynamic control variable through which the system can be stabilized over time.

Draft available upon request.

SIGNAL PREFERENCE IN MEAN-FIELD GAMES WITH DYNAMIC ENDOGENOUS PRECISION

WITH DANIEL CONUS (DEPARTMENT OF MATHEMATICS, LEHIGH UNIVERSITY)

This project builds on our dynamic signal precision framework while relaxing the assumption of homogeneous Bayesian agents. Rather than categorizing heterogeneous agents by risk preference, we classify them by signal preference—confirmatory versus contradictory signals. The motivation is twofold. First, gain-seeking and loss-avoidance are common features of human behavior, so risk preference alone may not be the most realistic basis for heterogeneity. Second, in modern information environments, agents are increasingly shaped by the signals they are fed, filtered into, and repeatedly exposed to. A more realistic source of heterogeneity therefore lies in the types of signals agents attend to.

Within this framework, we model signal preference as an endogenous reflection of prior confidence: relatively confident agents tilt toward confirmatory signals, while more self-reflective agents—more sensitive to negative or opposing information—tilt toward contradictory signals. We formulate the problem as a mean-field stochastic game in which heterogeneous agents choose precision endogenously and interact through the aggregate evolution of beliefs and portfolio behavior in the population. Confirmatory types reinforce priors until sufficiently large shocks trigger discrete corrections, whereas contradictory types revise beliefs more skeptically in response to disconfirming signals. One conjecture is that, despite sharply different updating paths, the two types may converge toward similar long-run portfolio behavior under common survival, cost, and feedback constraints. One possible mechanism is a symmetry in cumulative information costs: skeptical agents front-load epistemic effort, whereas confirmatory types defer it, so that total cognitive investment may become comparable over the decision horizon.