Related papers: Finite-time ruin probability of aggregate Gaussian…

For a bivariate L\'evy process $(\xi_t,\eta_t)_{t\geq 0}$ the generalised Ornstein-Uhlenbeck (GOU) process is defined as V_t:=e^{\xi_t}(z+\int_0^t e^{-\xi_{s-}}d\eta_s), t\ge0, where $z\in\mathbb{R}.$ We define necessary and sufficient…

We study a dynamic model of a non-life insurance portfolio. The foundation of the model is a compound Poisson process that represents the claims side of the insurer. To introduce clusters of claims appearing, e.g. with catastrophic events,…

Let X be a second order random process indexed by a compact interval [0,T]. Assume that n independent realizations of X are observed on a fixed grid of p time points. Under mild regularity assumptions on the sample paths of X, we show the…

Consider a random walk $S_n=\sum_{i=1}^n X_i$ with independent and identically distributed real-valued increments with zero mean, finite variance and moment of order $2 + \delta$ for some $\delta>0$. For any starting point $x\in \mathbb R$,…

Let $(W_1(s), W_2(t)), s,t\ge 0$ be a bivariate Brownian motion with standard Brownian motion marginals and constant correlation $\rho \in (-1,1).$ In this contribution we derive precise approximations for cumulative Parisian ruin…

This paper studies risk balancing features in an insurance market by evaluating ruin probabilities for single and multiple components of a multivariate compound Poisson risk process. The dependence of the components of the process is…

This paper considers a Cram\'er-Lundberg risk setting, where the components of the underlying model change over time. These components could be thought of as the claim arrival rate, the claim-size distribution, and the premium rate, but we…

We examine hitting probability problems for Ornstein-Uhlenbeck (OU) processes and Geometric Brownian motions (GBM) with respect to exponential boundaries related to problems arising in risk theory and asset and liability models in pension…

We prove that a large class of discrete-time insurance surplus processes converge weakly to a generalized Ornstein-Uhlenbeck process, under a suitable re-normalization and when the time-step goes to 0. Motivated by ruin theory, we use this…

Let $\boldsymbol{X}(t)=(X_1(t),\ldots,X_d(t))$ be a Gaussian vector process and $g(t)$ be a continuous function. The asymptotics of distribution of $\left\|\boldsymbol{X}(t)\right\|_p$, the $L^p$ norm for Gaussian finite-dimensional vector,…

For a bivariate \Levy process $(\xi_t,\eta_t)_{t\geq 0}$ the generalised Ornstein-Uhlenbeck (GOU) process is defined as \[V_t:=e^{\xi_t}(z+\int_0^t e^{-\xi_{s-}}\ud \eta_s), t\ge0,\]where $z\in\mathbb{R}.$ We present conditions on the…

Let $\{B(t), t\ge 0\}$ be a Brownian motion. Consider the Brownian motion risk model with interest rate collection and tax payment defined by \begin{align}\label{Rudef}…

Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem…

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…

The problem is a power-law asymptotics of the probability that a self-similar process does not exceed a fixed level during long time. The exponent in such asymptotics is estimated for some Gaussian processes, including the fractional…

In this work, we derive a complete characterization of all ruin-inducing probability measures that preserve the structure of a given compound renewal process in terms of suitable pairs of functions $(\gamma,\delta)$. This result allows us…

We study the asymptotics of the ruin probability in the Cram\'er-Lundberg model with a modified notion of ruin. The modification is as follows. If the portfolio becomes negative, the asset is not immediately declared ruined but may survive…

For $\{X(t), t \in G_\delta\}$ a centered Gaussian process with stationary increments and a.s. sample paths on a discrete grid $G_\delta=\{0,\delta,2\delta, ...\}$, where $\delta>0$, we investigate the stationary reflected process…

We consider the point process of zeroes of certain Gaussian analytic functions and find the asymptotics for the probability that there are more than m points of the process in a fixed disk of radius r, as m-->infinity. For the Planar…

The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in $n$ fixed points at $n$ fixed past instants. In particular, functional large deviation results are stated for small time. Several…