The main focus of this thesis is to develop full parametric and semiparametric Bayesian inference for data arising from triangular distributions. A natural consequence of working with such distributions is it allows one to consider regression models where the response variable is now the mode of the data distribution. A new family of nonparametric prior distributions is developed for a certain class of convex densities of particular relevance to mode regressions. Triangular distributions arise in several contexts such as geosciences, econometrics, finance, health care management, sociology, reliability engineering, decision and risk analysis, etc. In many fields, experts, typically, have a reasonable idea about the range and most likely values that define a data distribution. Eliciting these quantities is thus, generally, easier than eliciting moments of other commonly known distributions. Using simulated and actual data, applications of triangular distributions, with and without mode regressions, in some of the aforementioned areas are tackled. / text

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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.

Software maintenance is an important activity in software engineering. Over the decades, software maintenance costs have been continually reported to account for a large majority of software costs [Zelkowitz 1979, Boehm 1981, McKee 1984, Boehm 1988, Erlikh 2000]. This fact is not surprising. On the one hand, software environments and requirements are constantly changing, which lead to new software system upgrades to keep pace with the changes. On the other hand, the economic benefits of software reuse have encouraged the software industry to reuse and enhance the existing systems rather than to build new ones [Boehm 1981, 1999]. Thus, it is crucial for project managers to estimate and manage the software maintenance costs effectively. / Accurate cost estimation of software projects is one of the most desired capabilities in software development Process. Accurate cost estimates not only help the customer make successful investments but also assist the software project manager in coming up with appropriate plans for the project and making reasonable decisions during the project execution. Although there have been reports that software maintenance accounts for the majority of the software total cost, the software estimation research has focused considerably on new development and much less on maintenance. Now if we talk about real time software system(RTSS) development cost estimation and maintenance cost estimation is not much differ from simple software but some critical factor are considered for RTSS development and maintenance like response time of software for input and processing time to give correct output. As like simple software maintenance cost estimation existing models (i.e. Modified COCOMO-II) can be used but after inclusion of some critical parameters related to RTSS. A Hypothetical Expert input and an industry data set of eighty completed software maintenance projects were used to build the model for RTSS maintenance cost. The full model, which was derived through the Bayesian analysis, yields effort estimates within 30% of the actual 51% of the time,outperforming the original COCOMO II model when it was used to estimate theseprojects by 34%. Further performance improvement was obtained when calibrating the full model to each individual program, generating effort estimates within 30% of the actual 80% of the time.

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