An Optimal Control Derivation of Nonlinear Smoothing Equations

The purpose of this paper is to review and highlight some connections between the problem of nonlinear smoothing and optimal control of the Liouville equation. The latter has been an active area of recent research interest owing to work in mean-field games and optimal transportation theory. The nonlinear smoothing problem is considered here for continuous-time Markov processes. The observation process is modeled as a nonlinear function of a hidden state with an additive Gaussian measurement noise. A variational formulation is described based upon the relative entropy formula introduced by Newton and Mitter. The resulting optimal control problem is formulated on the space of probability distributions. The Hamilton's equation of the optimal control are related to the Zakai equation of nonlinear smoothing via the log transformation. The overall procedure is shown to generalize the classical Mortensen's minimum energy estimator for the linear Gaussian problem.Comment: 7 pages, 0 figures, under peer reviewin

Deducing the Multi-Trader Population Driving a Financial Market

We previously laid out a framework for predicting financial movements and pockets of predictability by deducing the heterogeneity in the multi-agent population in temrs of trader types playing in an artificial financial market model [7]. This work explores extensions to this basic framework. We allow for more intelligent agents with a richer strategy set, and we no longer constrain the estimate for the heterogeneity over the agents to a probability space. We then introduce a scheme which accounts for models with a wide variety of agent types. We also discuss a mechanism for bias removal on the estimates of the relevant parameters

Sustaining Economic Exploitation of Complex Ecosystems in Computational Models of Coupled Human-Natural Networks

Understanding ecological complexity has stymied scientists for decades. Recent elucidation of the famously coined "devious strategies for stability in enduring natural systems" has opened up a new field of computational analyses of complex ecological networks where the nonlinear dynamics of many interacting species can be more realistically mod-eled and understood. Here, we describe the first extension of this field to include coupled human-natural systems. This extension elucidates new strategies for sustaining extraction of biomass (e.g., fish, forests, fiber) from ecosystems that account for ecological complexity and can pursue multiple goals such as maximizing economic profit, employment and carbon sequestration by ecosystems. Our more realistic modeling of ecosystems helps explain why simpler "maxi-mum sustainable yield" bioeconomic models underpinning much natural resource extraction policy leads to less profit, biomass, and biodiversity than predicted by those simple models. Current research directions of this integrated natu-ral and social science include applying artificial intelligence, cloud computing, and multiplayer online games