Perturbation spreading in many-particle systems: a random walk approach

The propagation of an initially localized perturbation via an interacting many-particle Hamiltonian dynamics is investigated. We argue that the propagation of the perturbation can be captured by the use of a continuous-time random walk where a single particle is traveling through an active, fluctuating medium. Employing two archetype ergodic many-particle systems, namely (i) a hard-point gas composed of two unequal masses and (ii) a Fermi-Pasta-Ulam chain we demonstrate that the corresponding perturbation profiles coincide with the diffusion profiles of the single-particle L\'{e}vy walk approach. The parameters of the random walk can be related through elementary algebraic expressions to the physical parameters of the corresponding test many-body systems

A model of corporate liquidity

We study a continuous time model of a levered firm with fixed assets generating a cash flow which fluctuates with business conditions. Since external finance is costly, the firm holds a liquid (cash) reserve to help survive periods of poor business conditions. Holding liquid assets inside the firm is costly as some of the return on such assets is dissipated due to agency problems. We solve for the firms optimal dividend, share issuance, and liquid asset holding policies. The firm optimally targets a level of liquid assets which is a non-monotonic function of business conditions. In good times, the firm does not need a high liquidity reserve, but as conditions deteriorate, it will target higher reserve. In very poor conditions, the firm will declare bankruptcy, usually after it has depleted its liquidity reserve. Our model can predict liquidity holdings, leverage ratios, yield spreads, expected default probabilities, expected loss given default and equity volatilities all in line with market experience. We apply the model to examine agency conflicts associated with the liquidity re-serve, and some associated debt covenants. We see that a restrictive covenant applied to the liquidity reserve will often enhance the debt value as well as the equity value

Sustainability in Uncertain Economies

Comprehensive wealth, Project evaluation, Resilience, Sustainable development, Uncertainty,