相关论文: Finite Time Ruin Probabilities for Tempered Stable…

We study a Sparre Andersen model in which the business activity of the company is described by a compound renewal process with drift assuming that the capital reserves are invested in a risky asset. The price of the latter is assumed to…

For two nonstandard renewal risk models, we investigate the precise large deviations of the finite-time ruin probability and a random sum of the net-loss process, and the asymptotics of the random-time ruin probability. Notably, in one of…

We study the exit time $\tau=\tau_{(0,\infty)}$ for 1-dimensional strictly stable processes and express its Laplace transform at $t^\alpha$ as the Laplace transform of a positive random variable with explicit density. Consequently, $\tau$…

In this note we give, for a spectrally negative Levy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below zero, with a length that exceeds a certain…

In this work we consider Bayesian inference problems with intractable likelihood functions. We present a method to compute an approximate of the posterior with a limited number of model simulations. The method features an inverse Gaussian…

We study the ruin problem over a risk process described by a discrete-time Markov model. In contrast to previous studies that focused on the asymptotic behaviour of ruin probabilities for large values of the initial capital, we provide a…

In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level $0$) up to an (independent) exponential horizon for spectrally negative L\'{e}vy risk processes and refracted spectrally…

In this paper we propose new iterative algorithm of calculating the joint distribution of the Parisian ruin time and the number of claims until Parisian ruin for the classical risk model. Examples are provided when the generic claim size is…

Important models in insurance, for example the Carm{\'e}r--Lundberg theory and the Sparre Andersen model, essentially rely on the Poisson process. The process is used to model arrival times of insurance claims. This paper extends the…

We analyze the distance $\mathcal{R}_T(u)$ between the first and the last passage time of $\{X(t)-ct:t\in [0,T]\}$ at level $u$ in time horizon $T\in(0,\infty]$, where $X$ is a centered Gaussian process with stationary increments and…

We consider a generalization of the classical risk model when the premium intensity depends on the current surplus of an insurance company. All surplus is invested in the risky asset, the price of which follows a geometric Brownian motion.…

In this article we derive formula for probability $\Prob(\sup_{t\leq T} (X(t)-ct)>u)$ where $X=\{X(t)\}$ is a spectrally positive L\'evy process and $c\in\RL$. As an example we investigate the inverse Gaussian L\'evy process.

Define a $\gamma$-reflected process $W_\gamma(t)=Y_H(t)-\gamma\inf_{s\in[0,t]}Y_H(s)$, $t\ge0$ with input process $\{Y_H(t), t\ge 0\}$ which is a fractional Brownian motion with Hurst index $H\in (0,1)$ and a negative linear trend. In risk…

Tempered stable distributions are frequently used in financial applications (e.g., for option pricing) in which the tails of stable distributions would be too heavy. Given the non-explicit form of the probability density function,…

We analyse the asymptotics of ruin probabilities of two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions when the initial reserves of both companies tend…

We investigate the probability that an insurance portfolio gets ruined within a finite time period under the assumption that the r largest claims are (partly) reinsured. We show that for regularly varying claim sizes the probability of ruin…

We consider a refracted jump diffusion process having two-sided jumps with rational Laplace transforms. For such a process, by applying a straightforward but interesting approach, we derive formulas for the Laplace transform of its…

We investigate the asymptotic of ruin probabilities when the company invests its reserve in a risky asset with a switching regime price. We assume that the asset price is a conditional geometric Brownian motion with parameters modulated by…

We consider an insurance company in the case when the premium rate is a bounded non-negative random function $c_\zs{t}$ and the capital of the insurance company is invested in a risky asset whose price follows a geometric Brownian motion…

Let (X_t, t>=0) be a Levy process started at 0, with Levy measure nu and T_x the first hitting time of level x>0: T_x:=inf{t>=0; X_t>x}. Let $F(theta, mu, rho,.) be the joint Laplace transform of (T_x, K_x, L_x): F(theta,mu,rho,x)…