Related papers: A characterization of equivalent martingale probab…
Dealing with compound renewal process with generally distributed jump sizes and inter-renewal intervals, we focus on the approximation for the fixed-probability level, which is the core of inverse level crossing problem. We are developing…
We study a multidimensional renewal risk model, with common counting process and cadlag returns. Considering that the claim vectors have common distribution from some multivariate distribution class with heavy tail, are mutually weakly…
This paper presents a convenient framework for modeling default process and pricing derivative securities involving credit risk. The framework provides an integrated view of credit valuation adjustment by linking distance-to-default,…
This paper concerns an insurance firm's surplus process observed at renewal inspection times, with a focus on assessing the probability of the surplus level dropping below zero. For various types of inter-inspection time distributions, an…
We introduce a novel framework to account for sensitivity to rewards uncertainty in sequential decision-making problems. While risk-sensitive formulations for Markov decision processes studied so far focus on the distribution of the…
In the paper, the martingales and super-martingales relative to a regular set of measures are systematically studied. The notion of local regular super-martingale relative to a set of equivalent measures is introduced and the necessary and…
We analyze the general L\'{e}vy insurance risk process for L\'{e}vy measures in the convolution equivalence class $\mathcal{S}^{(\alpha)}$, $\alpha>0$, via a new kind of path decomposition. This yields a very general functional limit…
We study a general perturbed risk process with cumulative claims modelled by a subordinator with finite expectation, with the perturbation being a spectrally negative Levy process with zero expectation. We derive a Pollaczek-Hinchin type…
We propose a novel approach in the assessment of a random risk variable $X$ by introducing magnitude-propensity risk measures $(m_X,p_X)$. This bivariate measure intends to account for the dual aspect of risk, where the magnitudes $x$ of…
For a $d$-dimensional stochastic process $(S_n)_{n=0}^N$ we obtain criteria for the existence of an equivalent martingale measure, whose density $z$, up to a normalizing constant, is bounded from below by a given random variable $f$. We…
We propose a general modeling framework for marked Poisson processes observed over time or space. The modeling approach exploits the connection of the nonhomogeneous Poisson process intensity with a density function. Nonparametric Dirichlet…
In this paper we investigate the Parisian ruin probability for an integrated Gaussian process. Under certain assumptions, we find the Parisian ruin probability and the classical ruin probability are on the log-scale asymptotically the same.…
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…
We propose that the entanglement of mixed states is characterised properly in terms of a probability density function $\mathcal{P}_{\rho}(\mathcal{E})$. There is a need for such a measure since the prevalent measures (such as…
We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the…
This paper obtains an asymptotic formula for the finite-time ruin probability of the compound nonhomogeneous Poisson risk model with a constant interest force, in which the claims are conditionally independent random variables with a common…
In this paper we consider the Parisian ruin probabilities for the dual risk model in a discrete-time setting. By exploiting the strong Markov property of the risk process we derive a recursive expression for the fnite-time Parisian ruin…
In this paper, we first define the multivariate tempered space-fractional Poisson process (MTSFPP) by time-changing the multivariate Poisson process with an independent tempered {\alpha}-stable subordinator. Its distributional properties,…
Experimentation involves risk. The investigator expends time and money in the pursuit of data that supports a hypothesis. In the end, the investigator may find that all of these costs were for naught and the data fail to reject the null.…
We are interested in the existence of equivalent martingale measures and the detection of arbitrage opportunities in markets where several multi-asset derivatives are traded simultaneously. More specifically, we consider a financial market…