Asymptotic analysis and optimization of some insurance modelsстатья
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Дата последнего поиска статьи во внешних источниках: 16 января 2019 г.
Аннотация: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 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 claims
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.