Regularity of invariant densities for 1D systems with random switching

© 2015 IOP Publishing Ltd & London Mathematical Society.This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove the smoothness of the invariant densities away from critical points and describe the asymptotics of the invariant densities at critical points.

Optimal Reporting Systems With Investor Information Acquisition

This paper analyzes a manager's optimal ex-ante reporting system using a Bayesian persuasion approach (Kamenica and Gentzkow (2011)) in a setting where investors affect cash flows through their decision to finance the firm's investment opportunities, possibly assisted by the costly acquisition of additional information (inspection). I examine how the informativeness and the bias of the optimal system are determined by investors' inspection cost, the degree of incentive alignment between the manager and the investor, and the prior belief that the project is profitable. I find that a mis-aligned manager's system is informative

only when the market prior is pessimistic and is always positively biased; this bias decreases as investors' inspection cost decreases. In contrast, a well-aligned manager's system is fully revealing when investors' inspection cost is high, and is counter-cyclical to the market belief when the inspection cost is low: It is positively (negatively) biased when the market belief is pessimistic (optimistic). Furthermore, I explore the extent to which the results generalize to a case with managerial manipulation and discuss the implications for investment efficiency. Overall, the analysis describes the complex interactions among determinants of firm disclosures and governance, and offers explanations for the mixed empirical results in this area.

Systematic characterization of thermodynamic and dynamical phase behavior in systems with short-ranged attraction

In this paper we demonstrate the feasibility and utility of an augmented version of the Gibbs ensemble Monte Carlo method for computing the phase behavior of systems with strong, extremely short-ranged attractions. For generic potential shapes, this approach allows for the investigation of narrower attractive widths than those previously reported. Direct comparison to previous self-consistent Ornstein-Zernike approximation calculations is made. A preliminary investigation of out-of-equilibrium behavior is also performed. Our results suggest that the recent observations of stable cluster phases in systems without long-ranged repulsions are intimately related to gas-crystal and metastable gas-liquid phase separation.