Optimizing reserves in school choice: A dynamic programming approach

We introduce a new model of school choice with reserves in which asocial planner is constrained by a limited supply of reserve seats and tries to find the matching that is optimal according to a social welfare function. We construct the optimal distribution of reserves via a quartic-time dynamic programming algorithm. Due to the modular nature of the algorithm, the resulting mechanism is strategy-proof for reserve-eligible students.     

Using the Black–Derman–Toy interest rate model for portfolio optimization

No-arbitrage interest rate models are designed to be consistent with the current term structure of interest rates. The diffusion of the interest rates is often approximated with a tree, in which the scenario-dependent fair price of any security is calculated as the present value of the risk-neutral expectation by backward induction. To use this tree in a portfolio optimization context it is necessary to account for the so-called “market price of risk”. In this paper we present a method to change the conditional probabilities in the Black–Derman–Toy model to the physical (or real) measure, including the market price of risk, and explore the economic implications for expected spot rates and for expected bond returns.     

Generating interest rate scenarios for bank asset liability management

Over the last years the Second European Directive on Banking and Financial services demand that financial institutions develop asset liability management tools to identify and measure the various financial risks they encounter. The present paper develops a goal programming ALM model with a simulation analysis, to assist a commercial bank in managing its exposure to interest rate risk taking into account a duration gap framework. An application of the ALM model takes place on a large commercial bank of Greece.     

The AURORA Financial Management System: Model and Parallel Implementation Design

The AURORA financial management system under development at the University of Vienna is a modular decision support tool for portfolio and asset–liability management. It is based on a multivariate Markovian birth-and-death factor model for the economic environment, a pricing model for the financial instruments and an objective function which is flexible enough to express risk aversion.The core of the system is a large scale linear or convex program, which due to its size and structure is well suited for parallel optimization methods.As the system is still at an early stage of development, the results are preliminary in nature. Only a few types of financial instruments are handled and just two types of objectives are considered. The parallel optimization modules are still in the development phase.     

Robust risk management

Estimating the probabilities by which different events might occur is usually a delicate task, subject to many sources of inaccuracies. Moreover, these probabilities can change over time, leading to a very difficult evaluation of the risk induced by any particular decision. Given a set of probability measures and a set of nominal risk measures, we define in this paper the concept of robust risk measure as the worst possible of our risks when each of our probability measures is likely to occur. We study how some properties of this new object can be related with those of our nominal risk measures, such as convexity or coherence. We introduce a robust version of the Conditional Value-at-Risk (CVaR) and of entropy-based risk measures. We show how to compute and optimize the Robust CVaR using convex duality methods and illustrate its behavior using data from the New York Stock Exchange and from the NASDAQ between 2005 and 2010.     

Strategic and operational decisions in restaurant revenue management

The paper addresses restaurant revenue management from both a strategic and an operational point of view. Strategic decisions in restaurants are mainly related to defining the most profitable combination of tables that will constitute the restaurant. We propose new formulations of the so-called “Tables Mix Problem” by taking into account several features of the real setting. We compare the proposed models in a computational study showing that restaurants, with the capacity of managing tables as renewable resources and of combining different-sized tables, can improve expected revenue performances. Operational decisions are mainly concerned with the more profitable assignment of tables to customers. Indeed, the “Parties Mix Problem” consists of deciding on accepting or denying a booking request from different groups of customers, with the aim of maximizing the total expected revenue. A dynamic formulation of the “Parties Mix Problem” is presented together with a linear programming approximation, whose solutions can be used to define capacity control policies based on booking limits and bid prices. Computational results compare the proposed policies and show that they lead to higher revenues than the traditional strategies used to support decision makers.     

Embedded options in commercial banking and their impact on asset liability management

Commercial bankers sell—more often give away—options to their clients like the prepayment facility attached to a mortgage or the right to obtain a credit at a prespecified interest rate which is associated in France with specific term deposits. This paper aims to present the financial consequences of these options from a microeconomic point of view and on the scale of the French banking system. We first example our valuation techniques and then analyse the impact on the balance sheet of a typical commercial bank, both in terms of value and sensitivity. Securitization is presented in this context as a way to monitor risk exposure. Finally the global impact of these embedded options in the French banking system is estimated and briefly discussed.     

稳健资产负债管理最优化模型及实证分析

本文提出一种新的稳健资产负债模型最优化模型.该模型考虑了利率的不确定性对未来现金流、资金成本和资产收益率的影响.我们通过构建情景树反映未来的利率变化的情景结构.由于最优决策对利率的预测十分敏感,我们提出系数预测值可在一定误差范围内的稳健资产负债最优化模型.实证分析结果表明,从收益与风险均衡的角度看,稳健优化模型产生的保守解优于系数确定的优化模型产生的最优解.     

Portfolio optimization under entropic risk management

framework in the risk uniqueness In this paper, properties of the entropic risk measure are examined rigorously in a general This risk measure is then applied in a dynamic portfolio optimization problem, appearing management constraint. By considering the dual problem, we prove the existence and of the solution and obtain an analytic expression for the solution.     

A general framework for multistage mean-variance post-tax optimization

An investor’s decisions affect the way taxes are paid in a general portfolio investment, modifying the net redemption value and the yearly optimal portfolio distribution. We investigate the role of these decisions on multistage mean-variance portfolio allocation model. A number of risky assets grouped in wrappers with special taxation rules is integrated in a multistage financial portfolio optimization problem. The uncertainty on the returns of assets is specified as a scenario tree generated by simulation/clustering based approach. We show the impact of decisions in the yearly reallocation of the investments for three typical cases with an annual fixed withdrawal in a fixed horizon that utilizes completely the option of taper relief offered by banks in UK. Our computational framework can be used as a tool for testing decisions in this context.     

Minimax and risk averse multistage stochastic programming

In this paper we study relations between the minimax, risk averse and nested formulations of multistage stochastic programming problems. In particular, we discuss conditions for time consistency of such formulations of stochastic problems. We also describe a connection between law invariant coherent risk measures and the corresponding sets of probability measures in their dual representation. Finally, we discuss a minimax approach with moment constraints to the classical inventory model.     

Optimal risk and liquidity management with costly refinancing opportunities

In this paper we study risk and liquidity management decisions within an insurance firm. Risk management corresponds to decisions regarding proportional reinsurance, whereas liquidity management has two components: distribution of dividends and costly equity issuance. Contingent on whether proportional or fixed costs of reinvestment are considered, singular stochastic control or stochastic impulse control techniques are used to seek strategies that maximize the firm value. We find that, in a proportional-costs setting, the optimal strategies are always mixed in terms of risk management and refinancing. In contrast, when fixed issuance costs are too high relative to the firm’s profitability, optimal management does not involve refinancing. We provide analytical specifications of the optimal strategies, as well as a qualitative analysis of the interaction between refinancing and risk management.     

Operations risk management by optimally planning the qualified workforce capacity

Operational risks are defined as risks of human origin. Unlike financial risks that can be handled in a financial manner (e.g. insurances, savings, derivatives), the treatment of operational risks calls for a “managerial approach”. Consequently, we propose a new way of dealing with operational risk, which relies on the well known aggregate planning model. To illustrate this idea, we have adapted this model to the case of a back office of a bank specializing in the trading of derivative products. Our contribution corresponds to several improvements applied to stochastic programming techniques. First, the model is transformed into a multistage stochastic program in order to take into account the randomness associated with the volume of transaction demand and with the capacity of work provided by qualified and non-qualified employees over the planning horizon. Second, as advocated by Basel II, we calculate the probability distribution based on a Bayesian Network to circumvent the difficulty of obtaining data which characterizes uncertainty in operations. Third, we go a step further by relaxing the traditional assumption in stochastic programming that imposes a strict independence between the decision variables and the random elements. Comparative results show that in general these improved stochastic programming models tend to allocate more human expertise in order to hedge operational risks. Finally, we employ the dual solutions of the stochastic programs to detect periods and nodes that are at risk in terms of the expertise availability.     

Capital adequacy and risk management in banking industry

The present paper deals with the issue of bank capital adequacy and risk management within a stochastic dynamic setting. In particular, an explicit risk aggregation and capital expression is provided regarding the portfolio choice and capital requirements special context. Such a framework leads to a nonlinear stochastic optimal control problem whose solution may be determined by means of dynamic programming algorithm. The pertaining analysis relies heavily on the stochastic dynamic modeling of such balance sheet items as securities, loans, and regulatory capital with stochastic interest rates. In this respect, the special Kalman filter approach is used for the purpose of estimating the model parameters. The reached findings reveal well that the Tunisian bank, subject of study, generally exceeds the minimum requirements and is adequately capitalized to maintain the appropriate capital amount level commensurate with the aggregate risk. Besides, empirical evidence on the regulations' impact on driving bank capitalization and risk‐taking behavior has also been highlighted. Copyright © 2015 John Wiley & Sons, Ltd.     

Network revenue management with inventory-sensitive bid prices and customer choice

We develop an approximate dynamic programming approach to network revenue management models with customer choice that approximates the value function of the Markov decision process with a non-linear function which is separable across resource inventory levels. This approximation can exhibit significantly improved accuracy compared to currently available methods. It further allows for arbitrary aggregation of inventory units and thereby reduction of computational workload, yields upper bounds on the optimal expected revenue that are provably at least as tight as those obtained from previous approaches. Computational experiments for the multinomial logit choice model with distinct consideration sets show that policies derived from our approach can outperform some recently proposed alternatives, and we demonstrate how aggregation can be used to balance solution quality and runtime.     

Impulsive control in management: Prospects and applications

An outline of impulsive control and its applications in management is reviewed. Conditions for optimal impulsive controls when the dynamic process is given by a stochastic differential equation with Wiener and jump processes are given. Applications to inventory control, capacity expansion, vehicle dispatching, maintenance-replacement-inspection, and pricing problems are formulated, and optimality conditions found. Although there are many other applications that can be outlined, these provide some motivation for further study in this emerging field.This work was supported by the European Institute for Advanced Studies in Management, Brussels, Belgium.     

Cost/risk balanced management of scarce resources using stochastic programming

We consider the situation when a scarce renewable resource should be periodically distributed between different users by a Resource Management Authority (RMA). The replenishment of this resource as well as users demand is subject to considerable uncertainty. We develop cost optimization and risk management models that can assist the RMA in its decision about striking the balance between the level of target delivery to the users and the level of risk that this delivery will not be met. These models are based on utilization and further development of the general methodology of stochastic programming for scenario optimization, taking into account appropriate risk management approaches. By a scenario optimization model we obtain a target barycentric value with respect to selected decision variables. A successive reoptimization of deterministic model for the worst case scenarios allows the reduction of the risk of negative consequences derived from unmet resources demand. Our reference case study is the distribution of scarce water resources. We show results of some numerical experiments in real physical systems.     

A vindication of centralized controls in inventory management

We study here a set of quasi-variational inequalities related to inventory/production stochastic problems. We mainly focus our attention on two subjects: (i) From a theoretical point of view, we compare the advantages of global controls versus a decentralized approach via a model of an inventory serial system with Gaussian demand. (ii) We consider discretized systems, we solve the simple model of (i), and we apply a similar technique for solving a more complex system with Poissonian demand. The centralized approach naturally leads to large-scale problems; we solve them using a fast algorithm of resolution with very good performances. We conclude with some numerical results.     

Time consistency and risk averse dynamic decision models: Definition,interpretation and practical consequences

This paper aims at resolving a major obstacle to practical usage of time-consistent risk-averse decision models. The recursive objective function, generally used to ensure time consistency, is complex and has no clear/direct interpretation. Practitioners rather choose a simpler and more intuitive formulation, even though it may lead to a time inconsistent policy. Based on rigorous mathematical foundations, we impel practical usage of time consistent models as we provide practitioners with an intuitive economic interpretation for the referred recursive objective function. We also discourage time-inconsistent models by arguing that the associated policies are sub-optimal. We developed a new methodology to compute the sub-optimality gap associated with a time-inconsistent policy, providing practitioners with an objective method to quantify practical consequences of time inconsistency. Our results hold for a quite general class of problems and we choose, without loss of generality, a CVaR-based portfolio selection application to illustrate the developed concepts.     

SLP-IOR: An interactive model management system for stochastic linear programs

In this paper stochastic linear programming (SLP) is considered from the model management point of view. General model management issues specific to SLP are discussed in connection with their implementation in SLP-IOR. The central topic of the paper is SLP-IOR itself which is a model management system for SLP being under development by the authors. The presentation is concentrated on single and two stage models these being the model classes incorporated into the present version of SLP-IOR.