ruin probability
Differential equations for ruin probability in a special risk model with FGM copula for the claim size and the inter claim time
... where ω(x, y), for all x, y ≥ , is the penalty function at the time of ruin for the surplus prior to ruin and the deficit at ruin, I(·) is the indicator function, and δ is a nonnegative parameter. We ...
13
CAS: Ruin Probability-Based Initial Capital of the Discrete-Time Surplus Process
... This paper studies an insurance model under the regulation that the insurance company has to reserve sufficient initial capital to ensure that ruin probability does not exceed the given quantity a . We ...
8
Upper Bound of Ruin Probability for an Insurance Discrete-Time Risk Model with Proportional Reinsurance and Investment
... time ruin probability based on the NWU ...of ruin probability in Theorem 1 is derived using the condition that “the Lundberg coefficient, R 0 exists, which satisfies Equation ...of ruin ...
20
Finite-time Ruin Probability of Renewal Model with Risky Investment and Subexponential Claims
... very famous asymptotic relation was established by Ver- averbeke (1979) and Embrechts and Veraverbeke (1982). Briefly speaking, they showed that, if the so-called safety loading condition holds and, the integrated tail ...
5
Finite Time Non-Ruin Probability Formulae for Erlang Claim Interarrivals and Continuous Interdependent Claim Severities
... In this paper, we consider a reasonably general risk model, in which claim inter- arrival times are assumed independent, non-identically Erlang distributed random variables with arbitrary shape and rate parameters, claim ...
28
Ruin Probability for Non-standard Poisson Risk Model with Stochastic Returns
... which extends (5) essentially. Jiang ([10]) extended some results to the risky case. See also Jiang ([8], [9]). Dufresne and Gerber ([4]) first researched the ruin probability for jump-diffusion Poisson ...
6
Minimizing Lundberg inequality for ruin probability under correlated risk model by investment and reinsurance
... company can derive an exponential upper bound estimation even if the net profit condi- tion (8) does not hold. This indicates that investment offers the insurance company more chance to control its exposure. Then, the ...
13
Dependent Risk Modelling and Ruin Probability: Numerical Computation and Applications
... finite-time ruin probability, but also the deficit at ...at ruin may be small, allowing the company to easily borrow and ...at ruin in the definition of alarm time allows one to emphasize only ...
109
Parisian ruin probability for Markov additive risk processes
... In this paper, we consider a spectrally negative Markov additive risk process. Using the theory of Jordan chain, a compact formula of Parisian ruin probability is given. The formula depends only on the ...
9
Two dimensional ruin probability for subexponential claim size
... of ruin probabilities of two in- surance companies (or two branches of the same company) that divide be- tween them both claims and premia in some specified proportions when the initial reserves of both companies ...
21
Minimizing an Insurer’s Ultimate Ruin Probability by Noncheap Proportional Reinsurance Arrangements and Investments
... This section discusses the numerical method to be applied in finding numerical solutions of the survival probability φ ( u ) using a fixed grid u = 0, h, 2h, . . .. The assumptions of Theorem 1 are assumed to hold ...
20
A Mixture-Exponential Approximation to Finite- and Infinite-time Ruin Probabilities of Compound Poisson Processes
... finite-time) ruin probability under a given compound Poisson surplus ...finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential ...
6
0k and the arrival of claims follows a Poisson process
... Yuen and Wang [9] derived an integro–differential equation for the Gerber–Shiu expected discounted penalty function, and then obtained an exact solution to the equation and also obtained closed form expressions for the ...
8
Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments
... conditional probability in finite time, martingale theory turns the nonlinear stochastic differential equation to a special class of boundary value problems defined by a parabolic equation with a nonsmooth coefficient ...
19
Ruin probabilities for a perturbed risk model with stochastic premiums and constant interest force
... In this example, η = . solves the equation θ (z) = , then the upper bounds for the model without investment could be obtained (see Remark .). However, we can find tighter bounds since r > . For example, when r ...
13
Gerber Shiu Function of Markov Modulated Delayed By Claim Type Risk Model with Random Incomes
... the ruin probability for the risk model decreases as the probability of the delay of by-claims is increasing, while in [2] the authors discussed the model perturbed by ...the ruin ...
14
On finite-time ruin probabilities in a generalized dual risk model with dependence
... Another important contribution of the paper is the result of Lemma B.1, which generalizes a previous result of Ignatov and Kaishev (2012), obtained for the case of Erlang claim amounts to the case of claim sizes ...
41
Applications of Mogulskii, and Kurtz Feng Large Deviation Results to Risk Reserve Processes with Aggregate Claims
... In this paper we examine the large deviations principle (LDP) for sequences of classic Cramér-Lundberg risk processes under suitable time and scale modifications, and also for a wide class of claim distributions ...
9
The Gerber-Shiu function in the perturbed compound Poisson Gamma Omega model with a dividend barrier
... of ruin, the surplus immediately before ruin, the deficit at ruin, the ruin probability, the Gerber-Shiu expected discounted penalty function, the expected discounted dividend payments ...
15
Some Results on a Double Compound Poisson Geometric Risk Model with Interference
... Motivated by the above findings, this study aims at gaining an insight into the effects of stochastic premium incomes under perturbation. In this paper, we will con- sider a double compound Poisson-Geometric risk model ...
5