Related papers: A characterization of equivalent martingale probab…
This note is a complement to the paper by Eberlein, Kabanov, and Schmidt on the asymptotic of the ruin probability in a Sparre Andersen non-life insurance model with investments a risky asset whose price follows a geometric L\'evy process.…
This work is concerned with forest and cumulant type expansions of general random variables on a filtered probability spaces. We establish a "broken exponential martingale" expansion that generalizes and unifies the exponentiation result of…
In the paper a problem of risk measures on a discrete-time market model with transaction costs is studied. Strategy effectiveness and shortfall risk is introduced. This paper is a generalization of quantile hedging presented in [4].
We derive sufficient conditions for the mixing of all orders of interacting transformations of a spatial Poisson point process, under a zero-type condition in probability and a generalized adaptedness condition. This extends a classical…
The generalized Poisson distribution is well known to be a compound Poisson distribution with Borel summands. As a generalization we present closed formulas for compound Bartlett and Delaporte distributions with Borel summands and a…
This article constructs a class of random probability measures based on exponentially and polynomially tilting operated on the laws of completely random measures. The class is proved to be conjugate in that it covers both prior and…
Using a suitable change of probability measure, we obtain a novel Poisson series representation for the arbitrage- free price process of vulnerable contingent claims in a regime-switching market driven by an underlying continuous- time…
In the present paper we study quantile risk measures and their domain. Our starting point is that, for a probability measure $ Q $ on the open unit interval and a wide class $ \mathcal{L}_Q $ of random variables, we define the quantile risk…
We study a continuous-time financial market with continuous price processes under model uncertainty, modeled via a family $\mathcal{P}$ of possible physical measures. A robust notion ${\rm NA}_{1}(\mathcal{P})$ of no-arbitrage of the first…
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 review basic modeling approaches for failure and maintenance data from repairable systems. In particular we consider imperfect repair models, defined in terms of virtual age processes, and the trend-renewal process which extends the…
We study multidimensional Cram\'er-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…
This paper investigates the Parisian ruin probability for processes with power-asymmetric behavior of the variance near the unique optimal point. We derive the exact asymptotics as the ruin boundary tends to infinity and extend the previous…
This note aims at presenting several new theoretical results for the compound Poisson point process, which follows the work of Zhang \emph{et al.} [Insurance~Math.~Econom.~59(2014), 325-336]. The first part provides a new characterization…
In actuarial practice, the usual independence assumptions for the collective risk model are often violated, implying a growing need for considering more general models that incorporate dependence. To this purpose, the present paper studies…
We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional…
In survival analysis, cure models have gained much importance due to rapid advancements in medical sciences. More recently, a subset of cure models, called destructive cure models, have been studied extensively under competing risks…
Let $\textbf{Z}(t)=(Z_1(t) ,\ldots, Z_d(t))^\top , t \in \mathbb{R}$ where $Z_i(t), t\in \mathbb{R}$, $i=1,...,d$ are mutually independent centered Gaussian processes with continuous sample paths a.s. and stationary increments. For…
Risk-neutral pricing dictates that the discounted derivative price is a martingale in a measure equivalent to the economic measure. The residual ambiguity for incomplete markets is here resolved by minimising the entropy of the price…
We consider the approximation of a convolution of possibly different probability measures by (compound) Poisson distributions and also by related signed measures of higher order. We present new total variation bounds having a better…