In this paper we analyze the so-called Parisian ruin probability, which arises when the surplus process stays below 0 longer than a fixed amount of time ζ > 0. We focus on a general spectrally negative Lévy insurance risk process. For this class of processes, we derive an expression for the ruin probability in terms of quantities that can be calculated explicitly in many models. We find its Cra...

In this paper we give an introduction to collective risk theory in its simplest form. Our aims are to indicate how some basic facts may be obtained by martingale methods and to point out some open problems

In this paper, we model the cash surplus (or equity) of a risky business with Brownian motion (with drift). Owners can take out in form “dividends”, subject to transaction costs. However, if hits 0 then ruin occurs and cannot operate any more. We consider two types dividend distributions: (i) periodic, regular ones (that is, dividends be paid only at countably many points time, according specif...

We consider that the surplus of an insurer follows compound Poisson process and the insurer would invest its surplus in risky assets, whose prices satisfy the Black-Scholes model. In the risk process, we decompose the ruin probability into the sum of two ruin probabilities which are caused by the claim and the oscillation, respectively. We derive the integro-differential equations for these rui...

In this paper, we study the discounted free Gerber-Shiu function for the compound binomial risk model with by-claims and randomized dividend policy. Specifically, explicit expression for the discounted free Gerber-Shiu function is obtained. This result allows us to derive formulae for some useful insurance quantities, including the ruin probability, the probability function of the deficit at ru...

The value of travel time savings (VTTS) is the monetary value attached to save a determined amount of travel time. VTTS is also the most important benefit category aimed at justifying investments in transport infrastructures by public administrations. Hence VTTS played a significant role in various economic studies, both analytical and empirical (Zamparini & Reggiani, 2007). "It is difficult to...

Risk theory refers to a body of techniques to model and measure the risk associated with a portfolio of insurance contracts. A first approach consists in modeling the distribution of total claims over a fixed period of time using the classical collective model of risk theory. A second input of interest to the actuary is the evolution of the surplus of the insurance company over many periods of ...