We consider an insurance portfolio situation in which there is possible dependence between the waiting time for a claim and its actual size. By employing underlying random walk structure we obtain explicit exponential estimates infinite- finite-time ruin probabilities case of light-tailed sizes. The results are illustrated several examples, worked out specific structures.

For a spectrally one-sided Lévy process, we extend various two-sided exit identities to the situation when process is only observed at arrival epochs of an independent Poisson process.In addition, consider problems this type for processes reflected either from above or below.The resulting Laplace transforms main quantities interest are in terms scale functions and turn out be simple analogues classical formulas.

In the framework of classical compound Poisson process in collective risk theory, we study a modification horizontal dividend barrier strategy by introducing random observation times at which dividends can be paid and ruin observed. This model contains both continuous-time discrete-time as limit represents certain type bridge between them still enables explicit calculation moments total discounted payments until ruin. Numerical illustrations for several sets parameters are given effect on...

Abstract In the framework of collective risk theory, we consider a compound Poisson model for surplus process where (and hence ruin) can only be observed at random observation times. For Erlang(n) distributed inter-observation times, explicit expressions discounted penalty function ruin are derived. The resulting contains both usual continuous-time and discrete-time as limiting cases, used an effective approximation scheme latter. Numerical examples given that illustrate effect times on...

Using fluctuation theory, we solve the two-sided exit problem and identify ruin probability for a general spectrally negative Lévy risk process with tax payments of loss-carry-forward type. We study arbitrary moments discounted total amount determine surplus level to start taxation which maximises expected aggregate income authority in this model. The results considerably generalise those Cramér-Lundberg model tax.

Abstract This paper characterizes irreducible phase-type representations for exponential distributions. Bean and Green (2000) gave a set of necessary sufficient conditions distribution with an generator matrix to be exponential. We extend these representations, we thus give characterization all consider the results in relation time-reversal distributions, PH-simplicity, algebraic degree distribution, applications results. In particular under which Coxian becomes exponential, construct...

The Asian option pricing problem is a lot like the American put in 1970s. An payoff rather simple, and common, feature, but it messes up our clean, closed-form valuation equations. This situation apparently persistent source of annoyance to mathematicians other quants, who respond with an outpouring creativity, form theory, algorithms, approximate solutions. Although this may seem overkill for specific at hand, produces useful new ideas techniques general derivatives toolkit. In article,...

We consider a risk process R t where the claim arrival is superposition of homogeneous Poisson and Cox with shot noise intensity process, capturing effect sudden increases due to external events. The distribution aggregate size investigated under these assumptions. For both light-tailed heavy-tailed distributions, asymptotic estimates for infinite-time finite-time ruin probabilities are derived. Moreover, we discuss an extension model adaptive premium rule that dynamically adjusted according...