Sentence examples for surplus process from inspiring English sources

The surplus process modeled by a continuous-time Markov chain and an independent market-index process.

The surplus process is extended from a spectrally negative Lévy risk process to a spectrally negative Markov additive risk process.

In classical risk models, the surplus process usually relies on the assumption of independence between the claim size and the inter-claim time.

Note that in situations (1 -(4), the surplus process (U^{b}) will regenerate itself after the first period; whereas in (5 - 6), (U^{b}) will switch to (bar{U}^{b}).

The perturbed compound Poisson risk model, first proposed by Gerber [1], is an extension of the classical risk model by adding diffusion process to denote small volatility in the surplus process.

Then the insurer's surplus process is described as U t)=x+int_{0}^{t}c(s),mathrm{d}s-S t),mathrm{d}s-S tum_{n=1}^{N(t)}X_{n}) denotes the aggregate claims by time t.

However, in our risk models, the whole surplus processes are not Lévy processes anymore.

Generally speaking, adjustment coefficients are regarded as the safety indices of the surplus processes, they are the positive zero-roots of the adjustment coefficient functions.

In classical unidimensional Lundberg-type risk models, most of which assumed that the surplus processes are Lévy processes, the adjustment coefficient functions are obtained via martingale techniques: the cumulate generating functions (c.g.f.'s) of the net loss processes.

In this section, we study the moment-generating function (M u,y,b)), which has been discussed in various surplus processes; for example, see Albrecher et al. [11], Cheung (2008) etc.

A higher substrate concentration is required to avoid excess amounts of water, since a surplus of process water has a negative effect on both the environmental and economic aspects of the process [ 7].