Information relaxations and duality in stochastic dynamic programs

We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a "penalty" that punishes violations of nonanticipativity. In applications, the hope is that this relaxed version of the problem will be simpler to solve than the original dynamic program. The upper bounds provided by this dual approach complement lower bounds on values that may be found by simulating with heuristic policies. We describe the theory underlying this dual approach and establish weak duality, strong duality, and complementary slackness results that are analogous to the duality results of linear programming. We also study properties of good penalties. Finally, we demonstrate the use of this dual approach in an adaptive inventory control problem with an unknown and changing demand distribution and in valuing options with stochastic volatilities and interest rates. These are complex problems of significant practical interest that are quite difficult to solve to optimality. In these examples, our dual approach requires relatively little additional computation and leads to tight bounds on the optimal values. © 2010 INFORMS.

Optimal Capital Requirements in Financial Networks with Fire Sales

I explore and analyze a problem of finding the socially optimal capital requirements for financial institutions considering two distinct channels of contagion: direct exposures among the institutions, as represented by a network and fire sales externalities, which reflect the negative price impact of massive liquidation of assets.These two channels amplify shocks from individual financial institutions to the financial system as a whole and thus increase the risk of joint defaults amongst the interconnected financial institutions; this is often referred to as systemic risk. In the model, there is a trade-off between reducing systemic risk and raising the capital requirements of the financial institutions. The policymaker considers this trade-off and determines the optimal capital requirements for individual financial institutions. I provide a method for finding and analyzing the optimal capital requirements that can be applied to arbitrary network structures and arbitrary distributions of investment returns.

In particular, I first consider a network model consisting only of direct exposures and show that the optimal capital requirements can be found by solving a stochastic linear programming problem. I then extend the analysis to financial networks with default costs and show the optimal capital requirements can be found by solving a stochastic mixed integer programming problem. The computational complexity of this problem poses a challenge, and I develop an iterative algorithm that can be efficiently executed. I show that the iterative algorithm leads to solutions that are nearly optimal by comparing it with lower bounds based on a dual approach. I also show that the iterative algorithm converges to the optimal solution.

Finally, I incorporate fire sales externalities into the model. In particular, I am able to extend the analysis of systemic risk and the optimal capital requirements with a single illiquid asset to a model with multiple illiquid assets. The model with multiple illiquid assets incorporates liquidation rules used by the banks. I provide an optimization formulation whose solution provides the equilibrium payments for a given liquidation rule.

I further show that the socially optimal capital problem using the ``socially optimal liquidation" and prioritized liquidation rules can be formulated as a convex and convex mixed integer problem, respectively. Finally, I illustrate the results of the methodology on numerical examples and

discuss some implications for capital regulation policy and stress testing.

Increasing arousal enhances inhibitory control in calm but not excitable dogs

© 2015, Springer-Verlag Berlin Heidelberg.The emotional-reactivity hypothesis proposes that problem-solving abilities can be constrained by temperament, within and across species. One way to test this hypothesis is with the predictions of the Yerkes–Dodson law. The law posits that arousal level, a component of temperament, affects problem solving in an inverted U-shaped relationship: Optimal performance is reached at intermediate levels of arousal and impeded by high and low levels. Thus, a powerful test of the emotional-reactivity hypothesis is to compare cognitive performance in dog populations that have been bred and trained based in part on their arousal levels. We therefore compared a group of pet dogs to a group of assistance dogs bred and trained for low arousal (N = 106) on a task of inhibitory control involving a detour response. Consistent with the Yerkes–Dodson law, assistance dogs, which began the test with lower levels of baseline arousal, showed improvements when arousal was artificially increased. In contrast, pet dogs, which began the test with higher levels of baseline arousal, were negatively affected when their arousal was increased. Furthermore, the dogs’ baseline levels of arousal, as measured in their rate of tail wagging, differed by population in the expected directions. Low-arousal assistance dogs showed the most inhibition in a detour task when humans eagerly encouraged them, while more highly aroused pet dogs performed worst on the same task with strong encouragement. Our findings support the hypothesis that selection on temperament can have important implications for cognitive performance.