共找到 20 条结果
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 $(γ,δ)$. This result allows us to obtain an explicit representation of the infinite-time ruin probability as an expectation under any ruin-inducing probability measure. A key feature of our approach is that the construction of these measures does not rely on the existence of moment generating functions, and is therefore applicable to heavy-tailed claim size distributions. The proposed framework includes the classical Esscher transform as a special case.
We introduce the hybrid risk process, constructed via a time-change transformation applied to the solution of a hybrid stochastic differential equation. The framework covers several modern ruin settings, incorporating features like Markov-modulation and reserve-dependent parameters through an interdependent structure where the surplus level influences the dynamics of the background environment. The approach lets us define and analyze the Generalized Omega ruin model, a novel definition of insolvency that synthesizes concepts like Erlangian, cumulative Parisian and Omega ruin into a unified competing-risks framework. Finally, we show that the models are computationally tractable. By adapting recent matrix-analytic techniques, we provide an efficient way to compute a wide range of ruin-related quantities.
In this paper we investigate continuity properties for ruin probability in the classical risk model. Properties of contractive integral operators are used to derive continuity estimates for the deficit at ruin. These results are also applied to obtain desired continuity inequalities in the setting of continuous time surplus process perturbed by diffusion. In this framework, the ruin probability can be expressed as the convolution of a compound geometric distribution $K$ with a diffusion term. A continuity inequality for $K$ is derived and an iterative approximation for this ruin-related quantity is proposed. The results are illustrated by numerical examples.
The gambler's ruin problem for correlated random walks (CRW), both with and without delays, is addressed using the Optional Stopping Theorem for martingales. We derive closed-form expressions for the ruin probabilities and the expected game duration for CRW with increments $\{1,-1\}$ and for symmetric CRW with increments $\{1,0,-1\}$ (CRW with delays). Additionally, a martingale technique is developed for general CRW with delays. The gambler's ruin probability for a game involving bets on two arbitrary patterns is also examined.
An insurance company, as a risk bearer, is exposed to the likelihood of running into ruin. This is the situation where the initial surplus falls below zero. There is the need to find the required start-up capital to hedge against insolvency. Most researchers, irrespective of whether the test for claim dependency holds or not, assume claim independence in their computing of ruin probabilities to start up their initial capital. The objective of this study is to carry out comparative sensitivity analysis of ruin probability under both assumptions of dependence and independence, irrespective of whether the data exhibits independence or not, based on data from an insurance company in Ghana. Secondary data from an insurance company was obtained from the National Insurance Commission (NIC) for the period of 2013 to 2017. The study employed copulas to determine the claim dependence among the various insurance products and the company in general. The study concluded that when there is dependence in the claim data, computing the ruin probability based on the assumption of independence results in underestimation. Among the various insurance products, the most profitable insurance product was
We study multidimensional Cramér-Lundberg risk processes where agents, located on a large sparse network, receive losses form their neighbors. To reduce the dimensionality of the problem, we introduce classification of agents according to an arbitrary countable set of types. The ruin of any agent triggers losses for all of its neighbours. We consider the case when the loss arrival process induced by the ensemble of ruined agents follows a Poisson process with general intensity function that scales with the network size. When the size of the network goes to infinity, we provide explicit ruin probabilities at the end of the loss propagation process for agents of any type. These limiting probabilities depend, in addition to the agents' types and the network structure, on the loss distribution and the loss arrival process. For a more complex risk processes on open networks, when in addition to the internal networked risk processes the agents receive losses from external users, we provide bounds on ruin probabilities.
The paper deals with the ruin problem of an insurance company investing its capital reserve in a risky asset with the price dynamics given by a conditional geometric Brownian motion whose parameters depend on a Markov process describing a random variations in the economic and financial environments. We prove smoothness of the ruin probability as a function of the initial capital and obtain for it an integro-differential equation.
Applying excursion theory, we re-express several well studied fluctuation quantities associated to Parisian ruin problem for Lévy risk processes in terms of integrals with respect to excursion measure for spectrally negative Lévy process. We show that these new expressions reconcile with the previous results on Parisian ruin problem.
This paper presents a novel model for bivariate stochastic fluid processes that incorporate a ruin-dependent behavioral switch. Unlike typical models that assume a shared underlying process, our model allows each process to operate independently until a ruin event in one triggers a change in the other. We develop a mathematical framework for our model, exploring its properties and providing closed-form expressions for approximations of key performance metrics, particularly the joint law of the ruin times. Our approach introduces a class of compatible pathwise approximations to analyze ruin probabilities, which we subsequently study through a matrix-analytic framework.
In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance company). Modeling the risk processes of the insurance companies by Cramér-Lundberg processes we obtain the Laplace transform in space of the probability that either of the insurance companies is ruined in finite time. Subsequently, for exponentially distributed claims, we derive an explicit analytical expression for this joint ruin probability by explicitly inverting this Laplace transform. We also provide a characterization of the Laplace transform of the joint ruin time.
We consider a two-dimensional ruin problem where the surplus process of business lines is modelled by a two-dimensional correlated Brownian motion with drift. We study the ruin function $P(u)$ for the component-wise ruin (that is both business lines are ruined in an infinite-time horizon), where $u$ is the same initial capital for each line. We measure the goodness of the business by analysing the adjustment coefficient, that is the limit of $-\ln P(u)/u$ as $u$ tends to infinity, which depends essentially on the correlation $ρ$ of the two surplus processes. In order to work out the adjustment coefficient we solve a two-layer optimization problem.
We study the asymptotics of the ruin probability in the Cramér-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 due to certain mechanisms. Under a rather general assumption on the mechanism - satisfied by most such modified models from the literature - we study the relation of the asymptotics of the modified ruin probability to the classical ruin probability. This is done under the Cramér condition as well as for subexponential integrated claim sizes.
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 after reinsurance is also regularly varying in terms of the initial capital, and derive an explicit asymptotic expression for the latter. We establish this result by leveraging recent developments on sample-path large deviations for heavy tails. Our results allow, on the asymptotic level, for an explicit comparison between two well-known large-claim reinsurance contracts, namely LCR and ECOMOR. We finally assess the accuracy of the resulting approximations using state-of-the-art rare event simulation techniques.
Cloudflare built an AI agent workspace for its employees。 Now it’s open source
A massive magma reservoir has been detected deep beneath Tuscany, despite showing no obvious signs at the surface。 Scientists mapped the roughly 6,000-cubic-kilometer body using natural ground vibrations recorded by dozens of seismic sensors。 It poses no immediate danger, but the discovery reveals how enormous volcanic systems can remain hidden and
Researchers have found a way to build much larger “twisted” oxide materials while precisely controlling how their atomic layers line up。 Because these materials can be made over large areas and transferred onto different surfaces, the technique could help turn twistronics from a laboratory curiosity into a practical platform for next-generation ele
A surprisingly simple change could make sodium-ion batteries far more powerful while opening the door to turning seawater into drinking water。 Researchers at the University of Surrey found that sodium vanadium oxide performs much better when its naturally occurring water is left inside instead of being removed during manufacturing
Rice University chemists have found a new way to make neodymium, a rare-earth metal, interact with oxygen。 Using a specially designed molecular structure described as a “basket,” the team positioned the atoms so they could form a bond once thought unlikely。 The breakthrough produced highly reactive compounds that could eventually give chemists alte
Dark matter particles may exert a hidden force on one another, but its effects are stranger than expected。 An extra attraction helps the particles cluster, yet it also makes dark matter effectively lighter as the Universe expands。 That weakens its gravitational impact and usually slows the growth of cosmic structure rather than accelerating it
Young Jupiter’s powerful magnetic field may have created a safe zone where several large moons could survive。 Saturn lacked this protection, possibly explaining why Titan stands almost alone among its largest moons