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http://dx.doi.org/10.5351/CSAM.2016.23.5.423

Stationary distribution of the surplus process in a risk model with a continuous type investment  

Cho, Yang Hyeon (Department of Statistics, Sookmyung Women's University)
Choi, Seung Kyoung (Department of Statistics, Sookmyung Women's University)
Lee, Eui Yong (Department of Statistics, Sookmyung Women's University)
Publication Information
Communications for Statistical Applications and Methods / v.23, no.5, 2016 , pp. 423-432 More about this Journal
Abstract
In this paper, we stochastically analyze the continuous time surplus process in a risk model which involves a continuous type investment. It is assumed that the investment of the surplus to other business is continuously made at a constant rate, while the surplus process stays over a given sufficient level. We obtain the stationary distribution of the surplus level and/or its moment generating function by forming martingales from the surplus process and applying the optional sampling theorem to the martingales and/or by establishing and solving an integro-differential equation for the distribution function of the surplus level.
Keywords
risk model; surplus process; stationary distribution; integro-differential equation; martingale; optional sampling theorem;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
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