Related papers: On the integro-differential equation arising in th…
This paper investigates the Parisian ruin probability for processes with power-asymmetric behavior of the variance near the unique optimal point. We derive the exact asymptotics as the ruin boundary tends to infinity and extend the previous…
We study a risk sensitive control version of the lifetime ruin probability problem. We consider a sequence of investments problems in Black-Scholes market that includes a risky asset and a riskless asset. We present a differential game that…
This article studies in detail the solution of an integral equation due to Rongming et al. [13]. The methods involve complex analysis. As an application, we find the ruin probability of a given Bonus-Malus system in a steady state. We…
Parisian ruin probability in the classical Brownian risk model, unlike the standard ruin probability can not be explicitly calculated even in one-dimensional setup. Resorting on asymptotic theory, we derive in this contribution an…
In this note we consider the two-dimensional risk model introduced in Avram et al. \cite{APP08} with constant interest rate. We derive the integral-differential equations of the Laplace transforms, and asymptotic expressions for the finite…
The aim of this paper is to compare two asset allocation methods for a pension scheme during the decumulation phase in the simplified portfolio selection between a risky asset following a geometric Brownian motion and a riskless asset. The…
We study the rough asymptotic behaviour of a general economic risk model in a discrete setting. Both financial and insurance risks are taken into account. Loss during the first $n$ years is modelled as a random variable…
This note is an addendum to the work initiated by Promyslov on the integro-differential equation arising in the ruin problem for annuity payment models. First, the existence of viscosity solutions is proved. Then the regularity of these…
We investigate the role of reinsurance in maximizing the wealth of an insurance company. We use Liu's uncertainty theory (B. Liu, 2007) for the problem modeling and follow-up computations. The uncertainty measure of ruin for the insurance…
We introduce a longevity feature to the classical optimal dividend problem by adding a constraint on the time of ruin of the firm. We extend the results in \cite{HJ15}, now in context of one-sided L\'evy risk models. We consider de…
This note explores the mathematical theory to solve modern gamblers ruin problems. We establish a ruin framework and solve for the probability of bankruptcy. We also show how this relates to the expected time to bankruptcy and review the…
We study the asymptotic of the ruin probability for a process which is the solution of linear SDE defined by a pair of independent L\'evy processes. Our main interest is the model describing the evolution of the capital reserve of an…
We analyse the ruin probabilities for a renewal insurance risk process with inter-arrival time distributions depending on the claims that arrived within a fixed (past) time window. This dependence could be explained through a regenerative…
We apply the theory of linear recurrence sequences to find an expression for the ultimate ruin probability in a discrete-time risk process. We assume the claims follow an arbitrary distribution with support $\{0,1,\ldots,m\}$, for some…
The present work concerns the finite-time ruin probabilities for several bidimensional risk models with constant interest force and correlated Brownian motions.} Under the condition that the two Brownian motions $\{B_1(t), t\ge 0\}$ and…
In ruin theory, the net profit condition intuitively means that the incurred random claims on average do not occur more often than premiums are gained. The breach of the net profit condition causes guaranteed ruin in few but simple cases…
In this work, we consider extensions of the dual risk model with proportional gains by introducing a dependence structure between gain sizes and gain interrarrival times. Among others, we further consider the case where the proportional…
We start by showing that the finite-time absolute ruin probability in the classical risk model with constant interest force can be expressed in terms of the transition probability of a positive Ornstein-Uhlenbeck type process, say X. Our…
We consider the classical optimal dividends problem under the Cram\'er-Lundberg model with exponential claim sizes subject to a constraint on the time of ruin. We introduce the dual problem and show that the complementary slackness…
In this paper, we consider the perturbed renewal risk process. Systems of integro-differential equations for the Gerber-Shiu functions at ruin caused by a claim and oscillation are established, respectively. The explicit Laplase transforms…