This work investigates the factors that contribute to financial crises. We first study the Dow Jones index performance by grouping the daily adjusted closing value into a two-month window and finding several critical quantiles in each window. Then, we identify severe downturn in these quantiles and find that the 5th quantile is the best to identify financial crises. We then matched these quantiles with historical financial crises and gave a basic explanation about them. Next, we introduced all exogenous factors that could be related to the crises. Then, we applied a rapid Bayesian variable selection technique - Stochastic Search Variable Selection (SSVS) using a Bayesian logistic regression model. Finally, we analyzed the result of SSVS, leading to the conclusion that that the dummy variable we created for disastrous hurricane, crude oil price and gold price (GOLD) should be included in the model. / text

This dissertation focuses on three cases of the following two stage problem in the context of multi-product inventories of vertically differentiated products. In Stage 1 of the problem, the manager determines the optimal production quantities of different products when the demands are uncertain. In Stage 2 of the problem, the demands for different products are observed. Now, the manager meets the demand of each product using the inventory of the product or by carrying out a downward substitution from the inventories of higher performance products. The manager’s objective is to maximize the expected revenue from the decisions made at the two stages collectively. The first problem addressed in this dissertation focuses on the case when different products are produced simultaneously on the same set of machines due to random variations in the manufacturing process. These systems, referred to as co-production systems, are very common in the semi- conductor industry, the textile industry and the agriculture industry. For this problem, we provide an analytical solution to the two stage problem, and discuss managerial insights that are specific to co-production systems and are not extendible to multi-item inventories of products that can be ordered or manufactured independently. The second problem addressed in this dissertation focuses on the case when different products can be ordered or manufactured independently, and no constraints to meet minimum fill rate requirements or to restrict the total inventory below a certain level are present. We present an analytical solution to this problem. The third problem addressed in this dissertation focuses on the case when different products can be ordered or manufactured independently and fill rate constraints and total inventory constraints are present. When the demands are multivariate normal, we show that this two stage problem can be reduced to a non-linear program using some new results for the determination of partial expectations. We also extend these results to higher order moments of the multivariate distribution and discuss their applications in solving some common operations management problems. / text

This report discusses a multi-stage stochastic programming model that maximizes expected ending time profit assuming investors can forecast a bull or bear market trend. If an investor can always predict the market trend correctly and pick the optimal stochastic strategy that matches the real market trend, intuitively his return will beat the market performance. For investors with different levels of prediction accuracy, our analytical results support their decision of selecting the highest return strategy. Real stock prices of 154 stocks on 73 trading days are collected. The computational results verify that accurate prediction helps to exceed market return while portfolio profit drops if investors partially predict or forecast incorrectly part of the time. A sensitivity analysis shows how risk control requirements affect the investor's decision on selecting stochastic strategies under the same prediction accuracy. / text

Based on the survey of Taiwan’s international tourist hotels during 1997 to 2001, this study applies stochastic frontier approach incorporating inefficiency effects to estimate cost inefficiency of international tourist hotels in Taiwan. Two hypotheses of no inefficiency and no inefficiency effects are rejected by using likelihood-ratio test. These outcomes indicate that the model and assumptions set up in this study are statistically more appropriate. The empirical evidence shows that the average cost inefficiency score during 1997 to 2001 is 1.1468 which suggests that actual cost expenditure is approximately 1.1468 times of minimum cost with fixed outputs. In empirical findings between inefficiency effects and cost inefficiencies, the factors such as diversification of services, competitive circumstances, various types of travelers, belonging to a international hotel chain, and located in the scenic area would improve cost efficiencies of international tourist hotels. However, it would worsen cost efficiencies for international tourist hotels to setting up a branch or branches.

In this thesis we focus on Stochastic combinatorial Optimization Problems (SCOPs), a wide class of combinatorial optimization problems under uncertainty, where part of the information about the problem data is unknown at the planning stage, but some knowledge about its probability distribution is assumed. Optimization problems under uncertainty are complex and difficult, and often classical algorithmic approaches based on mathematical and dynamic programming are able to solve only very small problem instances. For this reason, in recent years metaheuristic algorithms such as Ant Colony Optimization, Evolutionary Computation, Simulated Annealing, Tabu Search and others, are emerging as successful alternatives to classical approaches. In this thesis, metaheuristics that have been applied so far to SCOPs are introduced and the related literature is thoroughly reviewed. In particular, two properties of metaheuristics emerge from the survey: they are a valid alternative to exact classical methods for addressing real-sized SCOPs, and they are flexible, since they can be quite easily adapted to solve different SCOPs formulations, both static and dynamic. On the base of the current literature, we identify the following as the key open issues in solving SCOPs via metaheuristics: (1) the design and integration of ad hoc, fast and effective objective function approximations inside the optimization algorithm; (2) the estimation of the objective function by sampling when no closed-form expression for the objective function is available, and the study of methods to reduce the time complexity and noise inherent to this type of estimation; (3) the characterization of the efficiency of metaheuristic variants with respect to different levels of stochasticity in the problem instances. We investigate the above issues by focusing in particular on a SCOP belonging to the class of vehicle routing problems: the Probabilistic Traveling Salesman Problem (PTSP). For the PTSP, we consider the Ant Colony Optimization metaheuristic and we design efficient local search algorithms that can enhance its performance. We obtain state-of-the-art algorithms, but we show that they are effective only for instances above a certain level of stochasticity, otherwise it is more convenient to solve the problem as if it were deterministic. The algorithmic variants based on an estimation of the objective function by sampling obtain worse results, but qualitatively have the same behavior of the algorithms based on the exact objective function, with respect to the level of stochasticity. Moreover, we show that the performance of algorithmic variants based on ad hoc approximations is strongly correlated with the absolute error of the approximation, and that the effect on local search of ad hoc approximations can be very degrading. Finally, we briefly address another SCOP belonging to the class of vehicle routing problems: the Vehicle Routing Problem with Stochastic Demands (VRPSD). For this problem, we have implemented and tested several metaheuristics, and we have studied the impact of integrating in them different ad hoc approximations.

No description available.

No description available.

This research studies two modelling techniques that help seek optimal strategies in financial risk management. Both are based on the stochastic programming methodology. The first technique is concerned with market risk management in portfolio selection problems; the second technique contributes to operational risk management by optimally allocating workforce from a managerial perspective. The first model involves multiperiod decisions (portfolio rebalancing) for an asset and liability management problem and deals with the usual uncertainty of investment returns and future liabilities. Therefore it is well-suited to a stochastic programming approach. A stochastic dominance concept is applied to control the risk of underfunding. A small numerical example and a backtest are provided to demonstrate advantages of this new model which includes stochastic dominance constraints over the basic model. Adding stochastic dominance constraints comes with a price: it complicates the structure of the underlying stochastic program. Indeed, new constraints create a link between variables associated with different scenarios of the same time stage. This destroys the usual tree-structure of the constraint matrix in the stochastic program and prevents the application of standard stochastic programming approaches such as (nested) Benders decomposition and progressive hedging. A structure-exploiting interior point method is applied to this problem. Computational results on medium scale problems with sizes reaching about one million variables demonstrate the efficiency of the specialised solution technique. The second model deals with operational risk from human origin. Unlike market risk 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 specialising in the trading of derivative products. Our contribution corresponds to several improvements applied to stochastic programming modelling. First, the basic 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 characterises 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. The dual solutions of the stochastic programs are exploited to detect periods and nodes that are at risk in terms of expertise availability.

This study gives a phenomenologically based stochastic model of space-time rainfall. Specifically, two random variables on the spatial rainfall, e.g., the cumulative rainfall within a season and the maximum cumulative rainfall per rainfall event within a season are considered. An approach is given to determine the cumulative distribution function (c.d.f.) of the cumulative rainfall per event, based on a particular random structure of space-time rainfall. Then the first two moments of the cumulative seasonal rainfall are derived based on a stochastic dependence between the cumulative rainfall per event and the number of rainfall events within a season. This stochastic dependence is important in the context of the spatial rainfall process. A theorem is then proved on the rate of convergence of the exact c.d.f. of the seasonal cumulative rainfall up to the iᵗʰ year, i ≥ 1, to its limiting c.d.f. Use of the limiting c.d.f. of the maximum cumulative rainfall per rainfall event up to the iᵗʰ year within a season is given in the context of determination of the 'design rainfall'. Such information is useful in the design of hydraulic structures. Special mathematical applications of the general theory are developed from a combination of empirical and phenomenological based assumptions. A numerical application of this approach is demonstrated on the Atterbury watershed in the Southwestern United States.

In this dissertation, we focus on developing sampling-based algorithms for solving stochastic linear programs. The work covers both two stage and multistage versions of stochastic linear programs. In particular, we first study the two stage stochastic decomposition (SD) algorithm and present some extensions associated with SD. Specifically, we study two issues: a) are there conditions under which the regularized version of SD generates a unique solution? and b) in cases where a user is willing to sacrifice optimality, is there a way to modify the SD algorithm so that a user can trade-off solution times with solution quality? Moreover, we present our preliminary approach to address these questions. Secondly, we investigate the multistage stochastic linear programs and propose a new approach to solving multistage stochastic decision models in the presence of constraints. The motivation for proposing the multistage stochastic decomposition algorithm is to handle large scale multistage stochastic linear programs. In our setting, the deterministic equivalent problems of the multistage stochastic linear program are too large to be solved exactly. Therefore, we seek an asymptotically optimum solution by simulating the SD algorithmic process, which was originally designed for two-stage stochastic linear programs (SLPs). More importantly, when SD is implemented in a time-staged manner, the algorithm begins to take the flavor of a simulation leading to what we refer to as optimization simulation. As for multistage stochastic decomposition, there are a couple of advantages that deserve mention. One of the benefits is that it can work directly with sample paths, and this feature makes the new algorithm much easier to be integrated within a simulation. Moreover, compared with other sampling-based algorithms for multistage stochastic programming, we also overcome certain limitations, such as a stage-wise independence assumption.