Cost and Reliability Approaches in Inventory Theory

Bulinskaya, Ekaterina

doi:10.1007/s10559-005-0041-8

Cited by 4 publications

(1 citation statement)

References 21 publications

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“…The most widely used approaches are reliability and cost ones, see, eg, the works of Bulinskaya and Afanasyeva and Bulinskaya . Thus, objective functions considered by researchers are either survival probability of the system under consideration and its lifetime until failure or costs (losses and profits) associated with the system functioning, see, eg, the work of Bulinskaya …”

Section: Introductionmentioning

confidence: 99%

Asymptotic analysis and optimization of some insurance models

Bulinskaya

2018

Appl Stoch Models Bus & Ind

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The aim of the paper is to show how one can perform asymptotic analysis of models arising in insurance, finance, and other applications of probability theory and solve optimization problems. To this end, we consider two insurance models (one continuous-time and one discrete-time). The first one is a dual Sparre Andersen insurance model with dividends. It describes not only the functioning of a life insurance company dealing with annuities but also a venture capital investment company or the capital of a business engaged in research and development. The main attention is paid to investigation of a new strategy of dividends payment. The second model deals with short-term credits in discrete-time case. We focus here on the system optimization in the framework of cost approach. In other words, expected discounted n-period costs are chosen as objective function. The optimal policy is obtained using dynamic programming. We introduce also the notion of asymptotic optimality and establish the form of asymptotically optimal policy. The model stability with respect to claim distribution perturbations is dealt with as well. Although we study only the simple cases, the methods proposed here can be useful for solving other optimization and stability problems. KEYWORDScost approach, dividends, insurance models, short-term credit INTRODUCTIONIt is well known to all the researchers dealing with applications that it is desirable to construct a mathematical model of a real-life process (or system) for its investigation. There can exist a lot of models describing the system with different degrees of accuracy. Moreover, the same model can arise in various research fields. Thus, methods applied in one domain can be useful in others.The models considered in such applications of probability theory as insurance, finance, queueing, reliability, inventory, dams, transport networks, population dynamics, and many others are of input-output type. In order to describe these models, see, eg, the work of Bulinskaya, 1 one has to ascertain input and output processes (or flows) and time horizon. To evaluate the system performance, one needs an objective function (target, valuation criterion, risk measure). It is also necessary to introduce a set of feasible controls and carry out the optimization.The most widely used approaches are reliability and cost ones, see, eg, the works of Bulinskaya 2 and Afanasyeva and Bulinskaya. 3 Thus, objective functions considered by researchers are either survival probability of the system under 762

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Section: Introductionmentioning

confidence: 99%