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Stochastic cash flows modelled by homogeneous and non-homogeneous discrete time backward semi-Markov reward processes

par Gismondi, Fulvio;Janssen, Jacques ;Manca, Raimondo;Volpe Di Prignano, Ernesto
Référence Sort, 38, 2, page (107-138)
Publication Publié, 2014-07

Article révisé par les pairs

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Résumé :

The main aim of this paper is to give a systematization on the stochastic cash flows evolution. The tools that are used for this purpose are discrete time semi-Markov reward processes. The paper is directed not only to semi-Markov researchers but also to a wider public, presenting a full treatment of these tools both in homogeneous and non-homogeneous environment. The main result given in the paper is the natural correspondence of the stochastic cash flows with the semi-Markov reward processes. Indeed, the semi-Markov environment gives the possibility to follow a multi-state random system in which the randomness is not only in the transition to the next state but also in the time of transition. Furthermore, rewards permit the introduction of a financial environment into the model. Considering all these properties, any stochastic cash flow can be naturally modelled by means of semi-Markov reward processes. The backward case offers the possibility of considering in a complete way the duration inside a state of the studied system and this fact can be very useful in the evaluation of insurance contracts.