### Working paper

## Optimal Dividend Policy When Cash Surplus Follows Telegraph Process

In a model of corporate finance introduced by Radner and Shepp and its numerous variations, the optimal dividend strategy was the main interest of research. Firm's dynamic properties like the probability of survival by the given time and the average ow of dividends recieved much less attention. We address these questions in a slightly modified Radner-Shepp model. Using the regularization of a Brownian motion with drift, which is, to our knowledge, new in the literature, we find the capital dynamics, the probability of survival by a given time, the average flow of dividends. We analyze the dependence of these indicators on firm's discount factor. © 2015 Igor G. Pospelov and Stanislav A. Radionov.

The paper contributes to the study of the features of temporary trends in stock indexes using an equilibrium approach with rational agents. It shows that the diffusion of significant fundamental information generates a Z-type aggregate demand function that leads to the occurrence of such a phenomenon as an imbalance (or disequilibrium). Pricing analysis under imbalance reveals that, with the exception of the independence of consecutive returns, there is a nonlinearity in mean that can be empirically detected using a threshold model or a regime switching model. The proposed model facilitates the convergence of the equilibrium approach with the methodology of evolutionary economics and can also be useful in studies of financial fragility.

This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching Markov chain. For this model, we 1) give finite sample bounds on the occupancy probabilities, and 2) provide detailed asymptotics in the case where the underlying distribution is regularly varying. We find that, in the regularly varying case, the finite sample bounds are rate optimal and have, up to a constant, the same rate of decay as the asymptotic result.