Identification and optimization of stochastic systems [electronic resource]
Keywords: Management Science and Engineering.

This dissertation centers on the identification and optimization of stochastic systems, both in static and dynamic settings. The leading application in this manuscript concerns models of consumer credit in unsecured debt markets. The first chapter provides an overview of the unsecured consumer debt market as well as the debt collection industry in the United States. The second chapter develops a mathematical framework for decision making in data-sparse settings. In data-sparse environments, the intersample behavior of the objective function is not well understood. This is in addition to intrasample uncertainty that exists because of the stochastic nature of the system or imperfect sampling technology. In such cases, structural insights in the form of monotonicity constraints over components of the objective function (e.g., a demand curve that is decreasing in price or a response curve that is increasing in a certain stimulus), obtained from model-based analysis of a decision problem, constitute the decision maker's principal form of knowledge. In this chapter, we develop a method to approximate decision problems, subject to structural monotonicity constraints, in view of robustly determining optimal actions. We furthermore design optimal robust experiments for the acquisition of additional data points. This method applies equally well in data-rich environments since interpolation and approximation are treated in a unified framework. The method is used to identify an optimal settlement offer for delinquent credit-card debts in a static setting. It predicts potential for at lease a 60% increase in the settlement yield when compared with the current practice. Motivated by the results of the static model, the third chapter develops a dynamic model of consumer repayment behavior on delinquent credit-card loans using a self-exciting marked point process. The model is used to construct a probability measure for the collectability of a delinquent account. The resulting account-specific dynamic collectability score (DCS) estimates, at any given time in the collection process, the probability of collecting a given percentage of the outstanding balance over a desired time horizon. This probability is conditional on repayment history, observed account-specific covariates such as FICO score, relevant macroeconomic data (e.g., interest rate), and collection strategy, all of which lay the foundation for account-treatment optimization. In addition to providing a flexible valuation framework for delinquent loans, DCS-based classification demonstrates a 30%--80% improvement over existing statistical models in identifying accounts capable of repaying their debts. Adopting the marked point process model developed in the third chapter, chapter four seeks to identify a compensation scheme that induces optimal account-level effort for collection agencies. The problem is formulated as a continuous-time principal-agent problem in which the agents (collection agencies) control the output process through a sequence of impulses (account-treatment actions). The principal (the credit-card issuer) can influence the agents by setting their commission rate. Moreover, each agent is contracted for a prespecified time. Upon expiry of a contract, the principal can revise the commission rate and assign an account to a different agent. In addition to providing a formulation, this chapter also provides preliminary results about properties of the principal-agent problems.