Stochastic Stability and Optimal Control of Semi-Markov Risk Processes in Insurance Mathematics

Anatoly Swishchuk
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Anatoly Swishchuk: National Academy of Sciences of Ukraine

Chapter Chapter 19 in Semi-Markov Models and Applications, 1999, pp 313-323 from Springer

Abstract: Abstract We study semi-Markov risk processes which describe a dynamic of summary capital of an insurance company. The theorems on stability, asymptotic and exponential stability of zero state of the processes with probability 1 are proved. We also investigate the optimal stochastic control of the controlled semi-Markov processes. The Bellman equation for semi-Markov risk processes is derived. Analogue of Dynkin formulae and boundary value problem for semi-Markov random evolutions, and properties of the respected stochastic Liapunov functions are used.

Keywords: Insurance mathematics; semi-Markov risk process; discontinuous semi-Markov random evolutions; analogue of Dynkin’s formula; boundary value problem; stochastic stability; optimal stochastic control; Bellman equation. (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-3288-6_19

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DOI: 10.1007/978-1-4613-3288-6_19

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