The Markovian regime-switching risk model with a threshold dividend strategy

Analysis of the Gerber–Shiu function and dividend barrier problems for a risk process with two classes of claims

“…It is observed now that (56) is a homogeneous integro-differential equation system and hence by similar arguments as previously (see also Eq. (6.7) for 0 ≤ u ≤ b in Lu and Li (2009)), it follows that the general solution of W m (u, b) and W m,1 (u, b) is given by…”

On the Markov-modulated insurance risk model with tax

“…. , d, are particular solutions to the following system of integro-differential equations: Note that v(u) = v 0 (u) and from [9] and [12] we know that whereˆ (s) = diag(λ 1f1 (y), λ 2f2 (y), . .…”

“…Ng and Yang [14] present some explicit results for the joint distribution of surplus before ruin and at ruin. Li and Lu [9], Zhu and Yang [16] and Lu and Li [12] consider the Markov-modulated risk model with a dividend strategy. Li and Lu [10] study the expected discounted penalty functions (Gerber-Shiu function) and their decompositions and the dividends-penalty identity under this model.…”

Dividend Payments and Related Problems in a Markov-Dependent Insurance Risk Model under Absolute Ruin

“…Li and Lu [4] study the moments of the present value of the dividend payments and the distribution of the total dividends prior to ruin for the Markov-modulated risk model modified by the introduction of a barrier dividend. Lu and Li [5] and Liu et al [6] consider a regime-switching risk model with a threshold dividend strategy. Zhu and Yang [7] study a more general Markovian regimeswitching risk model in which the premium, the claim intensity, the claim amount, the dividend payment rate and the dividend threshold level are influenced by an external Markovian environment process.…”