相关论文: A characterization of equivalent martingale probab…

Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…

Generalizing the realized variance, the realized skewness (Neuberger, 2012) and the realized kurtosis (Bae and Lee, 2020), we construct realized cumulants with the so-called aggregation property. They are unbiased statistics of the…

For a risk process $R_u(t)=u+ct-X(t), t\ge 0$, where $u\ge 0$ is the initial capital, $c>0$ is the premium rate and $X(t),t\ge 0$ is an aggregate claim process, we investigate the probability of the Parisian ruin \[…

Marginal structural models were introduced in order to provide estimates of causal effects from interventions based on observational studies in epidemiological research. The key point is that this can be understood in terms of Girsanov's…

What constitutes jointly Poisson processes remains an unresolved issue. This report reviews the current state of the theory and indicates how the accepted but unproven model equals that resulting from the small time-interval limit of…

Systemic risk is receiving increasing attention in the insurance industry. In this paper, we propose a multi-dimensional L\'{e}vy process-based renewal risk model with heterogeneous insurance claims, where every dimension indicates a…

This survey gives an introduction to monetary measures of risk as monotone and cash additive functions on spaces of univariate random variables. Primal and dual representation results as well as several examples are discussed. Principal…

The insurance model when the amount of claims depends on the state of the insured person (healthy, ill, or dead) and claims are connected in a Markov chain is investigated. The signed compound Poisson approximation is applied to the…

Let $L$ be a linear space of real bounded random variables on the probability space $(\Omega,\mathcal{A},P_0)$. There is a finitely additive probability $P$ on $\mathcal{A}$, such that $P\sim P_0$ and $E_P(X)=0$ for all $X\in L$, if and…

In this manuscript we propose a method for pricing insurance products that cover not only traditional risks, but also unforeseen ones. By considering the Poisson process parameter to be a mixed random variable, we capture the heterogeneity…

In this paper, we build on the techniques developed in Albrecher et al. (2013), to generate initial-boundary value problems for ruin probabilities of surplus-dependent premium risk processes, under a renewal case scenario, Erlang (2) claim…

This paper investigates the martingale characterizations of non-homogeneous counting processes and their fractional generalizations. We show that the weighted sum of non-homogeneous Poisson processes (NPPs) is the non-homogeneous…

In this text, we establish the risk model based on AR(1) series and propose the basic model which has a dependent structure under intensity of claim number. Considering some properties of the risk model, we take advantage of newton…

The discrete time risk model with two seasons and dependent claims is considered. An algorithm is created for computing the values of the ultimate ruin probability. Theoretical results are illustrated with numerical examples.

The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…

We consider a global market constituted by several submarkets, each with its own assets and num\'eraire. We provide theoretical foundations for the existence of equivalent martingale measures and results on superreplication prices which…

We deal with a generalization of the classical risk model when an insurance company gets additional funds whenever a claim arrives and consider some practical approaches to the estimation of the ruin probability. In particular, we get an…

We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of…

Marked point process data arise when events occur in a space with event-level marks. We study clustering of replicated marked Poisson point processes and introduce Dirichlet process mixtures of marked Poisson point processes, a Bayesian…

In this paper, we study the concept of Parisian ruin under the hybrid observation scheme model introduced by Li et al. \cite{binetal2016}. Under this model, the process is observed at Poisson arrival times whenever the business is…