A mixed integer linear programming model for optimal sovereign debt issuance

Copyright @ 2011, Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in the European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version is available at the link below.Governments borrow funds to finance the excess of cash payments or interest payments over receipts, usually by issuing fixed income debt and index-linked debt. The goal of this work is to propose a stochastic optimization-based approach to determine the composition of the portfolio issued over a series of government auctions for the fixed income debt, to minimize the cost of servicing debt while controlling risk and maintaining market liquidity. We show that this debt issuance problem can be modeled as a mixed integer linear programming problem with a receding horizon. The stochastic model for the interest rates is calibrated using a Kalman filter and the future interest rates are represented using a recombining trinomial lattice for the purpose of scenario-based optimization. The use of a latent factor interest rate model and a recombining lattice provides us with a realistic, yet very tractable scenario generator and allows us to do a multi-stage stochastic optimization involving integer variables on an ordinary desktop in a matter of seconds. This, in turn, facilitates frequent re-calibration of the interest rate model and re-optimization of the issuance throughout the budgetary year allows us to respond to the changes in the interest rate environment. We successfully demonstrate the utility of our approach by out-of-sample back-testing on the UK debt issuance data

A Stochastic Linear Programming Model for Asset Liability Management: The Case of an Indian Insurance Company

Asset - Liability management is one of the most critical tasks for any financial institution for determining its cushion against the risk and the net returns. The problem of asset liability management for an insurance company requires matching the cash inflows from premium collections and investment income with the cash outflows due to casualty and maturity claims. Thus, what is required is a prudent investment strategy such that the returns earned on the assets match the liability claims at all points of time in future. Conventionally, the asset allocation has been done using the Mean Variance approach due to Markowitz (1952, 1959). While such a strategy ensures that the asset value always match or are greater than the liability for the next year, it does not maximise the net worth of the firm nor does it take care of all the cash inflows and outflows over a long term period. A stochastic linear programming model (on the lines of Pirbhai, 2004) maximises the net worth of the firm and also takes care of the uncertainties. While there are instances of stochastic linear programming being applied for ALM in financial institutions in developed markets, no such practical application has been reported in this area in Indian context as yet. In this paper, we describe the development of a multi stage stochastic linear programming model for insurance companies. The multi-stage stochastic linear programming model was developed on the modelling language AMPL (Fourer, 2002).

DISCRETE STOCHASTIC PROGRAMMING: CONCEPTS, EXAMPLES AND A REVIEW OF EMPIRICAL APPLICATIONS

Research Methods/ Statistical Methods,

Applications of optimization to sovereign debt issuance

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel UniversityThis thesis investigates different issues related to the issuance of debt by sovereign bodies such as governments, under uncertainty about the future interest rates. Several dynamic models of interest rates are presented, along with extensive numerical experiments for calibration of models and comparison of performance on real financial market data. The main contribution of the thesis is the construction and demonstration of a stochastic optimisation model for debt issuance under interest rate uncertainty. When the uncertainty is modelled using a model from a certain class of single factor interest rate models, one can construct a scenario tree such that the number of scenarios grows linearly with time steps. An optimization model is constructed using such a one factor scenario tree. For a real government debt issuance remit, a multi-stage stochastic optimization is performed to choose the type and the amount of debt to be issued and the results are compared with the real issuance. The currently used simulation models by the government, which are in public domain, are also reviewed. Apparently, using an optimization model, such as the one proposed in this work, can lead to substantial savings in the servicing costs of the issued deb

Design of Availability Payment Mechanism for Public Private Partnerships

Availability Payment Public Private Partnerships (PPPs) are long-term contracts where the private sector is allocated responsibilities of designing, building, financing, operating and maintaining the highway on a public project. In return to their services the private sector is reimbursed through a performance-based predetermined payment plan. As per this plan, the private sector is entitled to receive predetermined payments called Maximum Availability Payments (MAPs) throughout the concession term (operations and maintenance phase). Thus the MAP amount and the length of concession term would have a major influence on the overall project cost since any inappropriate increase or decrease to these terms will heavily influence the project outcomes. This mandates the public agencies to diligently design MAPs and concession term but review of practices shows that the public agencies have been relying on unwarranted traditional methods to finalize these terms. Furthermore, very few researchers have worked towards designing the concession term and all the previous works have considered the payments and concession term as independent variables. Last, the timing and cost of post-concession maintenance costs have never been considered before while designing payment structure and concession term. This research work introduces a hybrid model developed by blending the stochastic dynamic programming model with multi-objective linear optimization principles that would allow the public sector to determine the upper limit of availability payments and concession term. This model ensures that public sector's cost saving objective and private sector's financial stability objective are satisfied simultaneously. The model also integrates post-concession maintenance cost structures and thus enables this model to include the effects of post-concession maintenance costs into the design. This model also allows inclusion of the effects of variation in private sector's financial condition and performance uncertainty in the design process. The research includes a case study focusing on Caltrans' Presidio Parkway Project and covers analyses that provide valuable insights about the design of Availability Payment PPPs. The analysis also quantifies and identifies the factors that affect payments and concession term in Availability Payment PPPs

SOME GUIDING PRINCIPLES FOR EMPIRICAL PRODUCTION RESEARCH IN AGRICULTURE

Constraints on production economic research are examined in three dimensions: problem focus, methodology, and data availability. Data availability has played a large role in the choice of problem focus and explains some misdirected focus. A proposal is made to address the data availability constraint. The greatest self-imposed constraints are methodological. Production economics has focused on flexible representations of technology at the expense of specificity in preferences. Yet some of the major problems faced by decision makers relate to long-term problems, e.g., the commodity boom and ensuring debt crisis of the 1970s and 1980s where standard short-term profit maximization models are unlikely to capture the essence of decision maker concerns.Production Economics,

Design of an Analysis Model for Strategic Behavior in the Digital Economy

Nowadays, multi-criteria decision-making techniques are highly developed, and are widely applied in multiple fields. They model and solve decisional problems by optimising multiple conflicting objectives. These techniques are very useful because they simultaneously analyse all the different criteria, and select the best alternatives according to the decision-maker’s objectives and preferences. An important issue in this context is the adequacy of the structure of corporate long-term financing and its potential impact on the sustainable development of the long-term business plan. The purpose of this study is to advance the analysis of these strategic decisions, measuring the a posteriori results and analysing their coherence with the strategies followed a priori. To do this, sustainable strategic decisions will be mathematically modelled and parametrised, creating a system to study the preferences followed and to describe the corporate behaviour. This system is applied as a case example for two leading companies in the digital sector, and the corresponding results over the last few years are evaluated