"Strategic Default Jump as Impulse Control in Continuous Time"

This paper presents a new approach for modeling an optimal debt contract in continuous time. It examines a competing contract design in a continuous-time environment with Markov income shocks and costly veri able information. It shows that an optimal contract has the form of a long-term debt contract that permits a debtor's strategic default and debt restructuring. The default is characterized by a recurrent, optimal impulse control beyond default. Numerical examples show that the equilibrium probability of the default is decreasing in the monitoring technology level when the default causes a big wealth loss.

Ergodic Control and Polyhedral approaches to PageRank Optimization

We study a general class of PageRank optimization problems which consist in finding an optimal outlink strategy for a web site subject to design constraints. We consider both a continuous problem, in which one can choose the intensity of a link, and a discrete one, in which in each page, there are obligatory links, facultative links and forbidden links. We show that the continuous problem, as well as its discrete variant when there are no constraints coupling different pages, can both be modeled by constrained Markov decision processes with ergodic reward, in which the webmaster determines the transition probabilities of websurfers. Although the number of actions turns out to be exponential, we show that an associated polytope of transition measures has a concise representation, from which we deduce that the continuous problem is solvable in polynomial time, and that the same is true for the discrete problem when there are no coupling constraints. We also provide efficient algorithms, adapted to very large networks. Then, we investigate the qualitative features of optimal outlink strategies, and identify in particular assumptions under which there exists a "master" page to which all controlled pages should point. We report numerical results on fragments of the real web graph.Comment: 39 page

A Generalized Decision Support System for the Contracting Career Field

This research effort develops a generalized decision support system (DSS) to assist contracting career field managers in making recruiting and retention decisions. The DSS focuses on the skill level inventories of the contracting enlisted force. The interest in this research was identified by contracting career field managers due to the recent negative trends in recruitment and retention and the lack of analytical tools available. To accomplish this objective manpower models were developed using a combination of techniques gathered through interviews with Army and Air Force analysts and a literature review focusing on manpower modeling. The models developed in this study are intended to assist career field managers in recruiting and retaining the correct number and skill level mix of personnel in the contracting career field. The models are generalized enough to serve as a DSS for other Air Force Specialty Codes (AFSC) with minimal revision

Algorithmic trading in a microstructural limit order book model

We propose a microstructural modeling framework for studying optimal market making policies in a FIFO (first in first out) limit order book (LOB). In this context, the limit orders, market orders, and cancel orders arrivals in the LOB are modeled as Cox point processes with intensities that only depend on the state of the LOB. These are high-dimensional models which are realistic from a micro-structure point of view and have been recently developed in the literature. In this context, we consider a market maker who stands ready to buy and sell stock on a regular and continuous basis at a publicly quoted price, and identifies the strategies that maximize her P\&L penalized by her inventory. We apply the theory of Markov Decision Processes and dynamic programming method to characterize analytically the solutions to our optimal market making problem. The second part of the paper deals with the numerical aspect of the high-dimensional trading problem. We use a control randomization method combined with quantization method to compute the optimal strategies. Several computational tests are performed on simulated data to illustrate the efficiency of the computed optimal strategy. In particular, we simulated an order book with constant/ symmet-ric/ asymmetrical/ state dependent intensities, and compared the computed optimal strategy with naive strategies. Some codes are available on https://github.com/comeh