Equivalence and bifurcations of finite order stochastic processes

This article presents an equivalence notion of finite order stochastic processes. Local dependence measures are defined in terms of ratios of joint and marginal probability densities. The dependence measures are classified topologically using level sets. The corresponding bifurcation theory is illustrated with some simple examples

A weak bifucation theory for discrete time stochastic dynamical systems

This article presents a bifurcation theory of smooth stochastic dynamical systems that are governed by everywhere positive transition densities. The local dependence structure of the unique strictly stationary evolution of such a system can be expressed by the ratio of joint and marginal probability densities; this ‘dependence ratio’ is a geometric invariant of the system. By introducing a weak equivalence notion of these dependence ratios, we arrive at a bifurcation theory for which in the compact case, the set of stable (nonbifurcating) systems is open and dense. The theory is illustrated with some simple examples

More hedging instruments may destabilize markets

This paper formalizes the idea that more hedging instruments may destabilize markets when traders are heterogeneous and adapt their behavior according to experience based reinforcement learning. We investigate three different economic settings, a simple mean-variance asset pricing model, a general equilibrium two-period overlapping generations model with heterogeneous expectations and a noisy rational expectations asset pricing model with heterogeneous information signals. In each setting the introduction of additional Arrow securities can destabilize the market, causing a bifurcation of the steady state to multiple steady states, periodic orbits or even chaotic fluctuations

Optimal Management with Potential Regime Shifts

We analyze how the threat of a potential future regime shift affects optimal management. We use a simple general growth model to analyze four cases that involve combinations of stock collapse versus changes in system dynamics, and exogenous versus endogenous probabilities of regime shift. Prior work has focused on stock collapse with endogenous probabilities and reaches ambiguous conclusions about the effect of potential regime shift on optimal management. We show that all other cases yield unambiguous results. In particular, with endogenous probability of regime shift that affects system dynamics the potential for regime shift causes optimal management to become precautionary