相关论文: A Note on the Ruin Problem with Risky Investments

In the setting of a L\'evy insurance risk process, we present some results regarding the Parisian ruin problem which concerns the occurrence of an excursion below zero of duration bigger than a given threshold $r$. First, we give the joint…

We consider the optimal investment problem when the traded asset may default, causing a jump in its price. For an investor with constant absolute risk aversion, we compute indifference prices for defaultable bonds, as well as a price for…

We consider a diffusion approximation to an insurance risk model where an external driver models a stochastic environment. The insurer can buy reinsurance. Moreover, investment in a financial market is possible. The financial market is also…

This paper focuses on a discrete-time risk model in which both insurance risk and financial risk are taken into account. We study the asymptotic behaviour of the ruin probability and the tail probability of the aggregate risk amount.…

This paper derives the asymptotic behavior of the following ruin probability $$P\{\exists t \in G(\delta):B_H(t)-c_1t>q_1u,B_H(t)-c_2t>q_2u\}, \ \ \ u \rightarrow \infty,$$ where $B_H$ is a standard fractional Brownian motion,…

Consider an insurance company exposed to a stochastic economic environment that contains two kinds of risk. The first kind is the insurance risk caused by traditional insurance claims, and the second kind is the financial risk resulting…

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…

In this paper we derive the exact asymptotics of the probability of Parisian ruin for self-similar Gaussian risk processes. Additionally, we obtain the normal approximation of the Parisian ruin time and derive an asymptotic relation between…

We consider an insurance company in the case when the premium rate is a bounded non-negative random function $c_\zs{t}$ and the capital of the insurance company is invested in a risky asset whose price follows a geometric Brownian motion…

The instability of the financial system as experienced in recent years and in previous periods is often linked to credit defaults, i.e., to the failure of obligors to make promised payments. Given the large number of credit contracts, this…

For two nonstandard renewal risk models, we investigate the precise large deviations of the finite-time ruin probability and a random sum of the net-loss process, and the asymptotics of the random-time ruin probability. Notably, in one of…

We used the random walk to model the problem of reserves. The classic case of a stochastic process is the example of random walks, which are used to study a set of phenomena and, particularly, as in this article, models of reserves…

In this paper, we generalise the results presented in the literature for the ruin probability for the insurer--reinsurer model under a pro-rata reinsurance contract. We consider claim amounts that are described by a phase-type distribution…

We analyse the asymptotics of ruin probabilities of two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions when the initial reserves of both companies tend…

This paper presents some new results on Parisian ruin under Levy insurance risk process, where ruin occurs when the process has gone below a fixed level from the last record maximum, also known as the high-water mark or drawdown, for a…

In this note, we explicitly solve the problem of maximizing utility of consumption (until the minimum of bankruptcy and the time of death) with a constraint on the probability of lifetime ruin, which can be interpreted as a risk measure on…

We reconsider a classical, well-studied problem from applied probability. This is the max-sum equivalence of randomly weighted sums, and the originality is because we manage to include interdependence among the primary random variables, as…

The problem of reconstructing the drift of a diffusion in $\erre^d$, $d\geq 2$, from the transition probability density observed outside a domain is considered. The solution of this problem also solves a new inverse problem for a class of…

In this paper, we discuss the Cram\'er-Lundberg model with investments, where the price of the invested risk asset follows a geometric Brownian motion with drift $a$ and volatility $\sigma> 0.$ By assuming there is a cap on the claim sizes,…

We consider a spectrally-negative Markov additive process as a model of a risk process in random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees…