This paper investigates the finite time ruin probability in non-homogeneous Poisson risk model, conditional Poisson risk models and renewal risk model with stochastic returns. Under the assumption that the claimsize is subexponentially distributed, a simple asymptotic relation is established when the initial capital tends to infinity. The results obtained extend the corresponding results of con...

Retirees who exhaust their savings while still alive are said to experience financial ruin. The savings are typically grown during life’s accumulation phase then spent during the retirement decumulation phase. Extensive research into invest-and-harvest decumulation strategies has been conducted, but recommendations differ markedly. This has likely been a source of concern and confusion for the ...

We find an exact asymptotics of the ruin probability Ψ(u) when the capital of insurance company is invested in a risky asset whose price follows a geometric Brownian motion with mean return a and volatility σ > 0. In contrast to the classical case of non-risky investments where the ruin probability decays exponentially as the initial endowment u tends to infinity, in this model we have, if ρ :=...

We consider the Erlang(λ, n) risk process with i.i.d. exponentially distributed claims severities. We prove that the ruin probability is a strictly decreasing function in n if we keep the expected interarrival times between two successive claims constant. In the limit case we obtain Lundberg’s fundamental equation in the discrete time risk model (ladder heights of random walks).

We consider the dynamic proportional reinsurance in a two-dimensional compound Poisson risk model. The optimization in the sense of minimizing the ruin probability which is defined by the sum of subportfolio is being ruined. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal value function and prove the verification theorem. In addition, we obtain the Lundberg bounds a...

This paper considered a dependent discrete-time risk model, in which the insurance risks are represented by a sequence of independent and identically distributed real-valued random variables with a common Gamma-like tailed distribution; the financial risks are denoted by another sequence of independent and identically distributed positive random variables with a finite upper endpoint, but a gen...

Consider N players, respectively owning x1, x2, . . . , xN monetary units, who play a sequence of games, winning from and losing to each other integer amounts according to fixed rules. The sequence stops as soon as (at least) one player is ruined. We are interested in the ruin process of theseN players, i.e. in the probability that a given player is ruined first, and also in the expected ruin t...

In this note we discuss upper and lower bound for the ruin probability in an insurance model with very heavy-tailed claims and interarrival times.

Thisstudy considered the Ruin problem with an income process stationaryindependent increments. The characterization is obtained which general forthe probability of r(y), that asset a firm will never bezero whenever initial level y. aim this studyis also to determine r(y) = P{T < ¥ | Y(0)= y}, If we let T inf{t ≥ 0; Y(t)< 0}, A condition necessary and sufficient studied for adistribution one – d...