Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact

This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we show that the function is continuous and has the semigroup property, which is strongly related to the Hamilton-Jacobi-Bellman quasi-variational inequality. Moreover, we show that noise in market impact causes risk-neutral assessment to underestimate the impact cost. We also study typical examples under a log-linear/quadratic market impact function with Gamma-distributed noise.Comment: 24 pages, 14 figures. Continuation of the paper arXiv:1301.648

Online Optimization with Memory and Competitive Control

This paper presents competitive algorithms for a novel class of online optimization problems with memory. We consider a setting where the learner seeks to minimize the sum of a hitting cost and a switching cost that depends on the previous p decisions. This setting generalizes Smoothed Online Convex Optimization. The proposed approach, Optimistic Regularized Online Balanced Descent, achieves a constant, dimension-free competitive ratio. Further, we show a connection between online optimization with memory and online control with adversarial disturbances. This connection, in turn, leads to a new constant-competitive policy for a rich class of online control problems

Optimal Timing in Banks' Write-Off Decisions under the Possible Implementation of a Subsidy Scheme: A Real Options Approach

This paper provides a formal model that investigates optimal timing in banks' writing off their nonperforming loans. The motivation comes from the recent episodes of Japanese banks, which have been slow to clean up their nonperforming loans after the collapse of the "bubble" economy in the early 1990s. A real options approach is employed to measure the value of the rationality of the "forbearance policy." It is assumed that uncertainty will arise from the following sources: (1) the reinvestment return from freeing up funds through write-offs; (2) liquidation losses; (3) the possible implementation of a subsidy scheme; and (4) the reputational repercussions from not immediately writing off their nonperforming loans. This paper attaches particular importance to the uncertainty from the possible implementation of the subsidy scheme to explore its desirable features. Also, this paper examines the possible role of monetary policy in boosting the banks' incentive to write off.

Feasibility-Guided Safety-Aware Model Predictive Control for Jump Markov Linear Systems

In this paper, we present a framework that synthesizes maximally safe control policies for Jump Markov Linear Systems subject to stochastic mode switches. Our approach builds on safe and robust methods for Model Predictive Control (MPC), but in contrast to existing approaches that either optimize without regard to feasibility or utilize soft constraints that increase computational requirements, we employ a safe and robust control approach informed by the feasibility of the optimization problem. When subject to inaccurate hybrid state estimation, our feasibility-guided MPC algorithm generates a control policy that is maximally robust to uncertainty in the system's modes. Additionally, we formulate the notion of safety guarantees for multiple-model receding horizon control using Control Barrier Functions (CBF) to enforce forward invariance in safety-critical settings. We simulate our approach on a six degree-of-freedom hexacopter under several scenarios to demonstrate the utility of the framework. Results illustrate that the proposed technique of maximizing the robustness horizon, and the use of CBFs for forward-invariance, improve the overall safety and performance of Jump Markov Linear Systems

Precautionary Effect and Variations of the Value of Information

For a sequential, two-period decision problem with uncertainty and under broad conditions (non-finite sample set, endogenous risk, active learning and stochastic dynamics), a general sufficient condition is provided to compare the optimal initial decisions with or without information arrival in the second period. More generally the condition enables the comparison of optimal decisions related to different information structures. It also ties together and clarifies many conditions for the so-called irreversibility effect that are scattered in the environmental economics literature. A numerical illustration with an integrated assessment model of climate-change economics is provided.Value of Information, Uncertainty, Irreversibility effect, Climate change

Sufficient Conditions for Feasibility and Optimality of Real-Time Optimization Schemes - II. Implementation Issues

The idea of iterative process optimization based on collected output measurements, or "real-time optimization" (RTO), has gained much prominence in recent decades, with many RTO algorithms being proposed, researched, and developed. While the essential goal of these schemes is to drive the process to its true optimal conditions without violating any safety-critical, or "hard", constraints, no generalized, unified approach for guaranteeing this behavior exists. In this two-part paper, we propose an implementable set of conditions that can enforce these properties for any RTO algorithm. This second part examines the practical side of the sufficient conditions for feasibility and optimality (SCFO) proposed in the first and focuses on how they may be enforced in real application, where much of the knowledge required for the conceptual SCFO is unavailable. Methods for improving convergence speed are also considered.Comment: 56 pages, 15 figure