In this paper, we generate boundary value problems for ruin probabilities of surplus-dependent premium risk processes, under a renewal case scenario, Erlang (2) claim arrivals, and a hypoexponential claims scenario, Erlang (2) claim sizes. Applying the approximation theory of solutions of linear...

In this paper, we generate boundary value problems for ruin probabilities of surplus-dependent premium risk processes, under a renewal case scenario, Erlang (2) claim arrivals, and a hypoexponential claims scenario, Erlang (2) claim sizes. Applying the approximation theory of solutions of linear...

In a virtual organization directed on the insurance business, the estimations of the risk process and of the ruin probability are important concerns: for researchers, at the theoretical level, and for the management of the company, as these influence the insurer strategy. We consider the...

In this paper, we extend the concept of ruin in risk theory to the Parisian type of ruin. For this to occur, the surplus process must fall below zero and stay negative for a continuous time interval of specified length. Working with a classical surplus process with exponential jump size, we...

In this paper, we extend the concept of ruin in risk theory to the Parisian type of ruin. For this to occur, the surplus process must fall below zero and stay negative for a continuous time interval of specified length. We obtain the probability of ruin in the infinite horizon for the case when...

In this paper we consider a jump-diffusion type approximation of the classical risk process by a gamma Levy process. We derive here the asymptotic behavior (lower and upper bounds) of the finite time ruin probability for any gamma Levy process.

One possible way of risk management for an insurance company is to develop an early and appropriate alarm system before the possible ruin. The ruin is defined through the status of the aggregate risk process, which in turn is determined by premium accumulation as well as claim settlement out-go...

We show how to solve Merton optimal investment stochastic control problem for Hawkesbased models in finance and insurance (Propositions 1 and 2), i.e., for a wealth portfolio X(t) consisting of a bond and a stock price described by general compound Hawkes process (GCHP), and for a capital R(t)...

Purpose of the article: The first part of the article shows summarised information on risk management in projects based on the literature review. The second part of the article is a case study made on the basis of materials made available by the company implementing the AZTiE project. The case...