Some results of ruin probability for the classical risk process.
Stability estimates of generalized geometric sums and their applications
The upper bounds of the uniform distance between two sums of a random number of independent random variables are given. The application of these bounds is illustrated by stability (continuity) estimating in models in queueing and risk theory.
Stable-1/2 bridges and insurance
We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an information-based approach to the reserving problem, we derive the process of the conditional distribution of the ultimate loss. The "best-estimate ultimate loss process" is given by the conditional expectation of the ultimate loss. We derive explicit expressions for the...
Stochastic dominance theory for location-scale family.
Subprime risk and insurance with regret.
Systemic risk through contagion in a core-periphery structured banking network
We contribute to the understanding of how systemic risk arises in a network of credit-interlinked agents. Motivated by empirical studies we formulate a network model which, despite its simplicity, depicts the nature of interbank markets better than a symmetric model. The components of a vector Ornstein-Uhlenbeck process living on the nodes of the network describe the financial robustnesses of the agents. For this system, we prove a LLN for growing network size leading to a propagation of chaos result....
The game as a contract and the “risicum" in the work of Olivi. (Le jeu comme contrat et le risicum chez Olivi.)
The martingale method of shortfall risk minimization in a discrete time market
The shortfall risk minimization problem for the investor who hedges a contingent claim is studied. It is shown that in case the nonnegativity of the final wealth is not imposed, the optimal strategy in a finite market model is obtained by super-hedging a contingent claim connected with a martingale measure which is a solution of an auxiliary maximization problem.
The Pólya-Aeppli process and ruin problems.
The problem of determining estimators for different structural parameters in the case of credibility results for weighted contracts
This paper presents and analyzes the estimators of the structural parameters, in the Bühlmann-Straub model, involving complicated mathematical properties of conditional expectations and of conditional covariances. So to enable to use the better linear credibility results obtained in this model, we will provide useful estimators for the structure parameters. From the practical point of view it is stated the attractive property of unbiasedness for these estimators.
Theoretical and practical considerations regarding bonus-malus system.
Two lognormal models for real data.
Valuation and optimal design to defaultable security
Herein, we develop a backward stochastic differential equation (BSDE) valuation of securities with default risk. Consequently, the optimal recovery problem with quasi-linear utility functions is discussed with the help of the stochastic maximum principle. Finally, two important examples: the exponential and power utility cases are studied and their business implications are considered.
VaR bounds for joint portfolios with dependence constraints
Based on a novel extension of classical Hoeffding-Fréchet bounds, we provide an upper VaR bound for joint risk portfolios with fixed marginal distributions and positive dependence information. The positive dependence information can be assumed to hold in the tails, in some central part, or on a general subset of the domain of the distribution function of a risk portfolio. The newly provided VaR bound can be interpreted as a comonotonic VaR computed at a distorted confidence level and its quality...
Virtual enterprise risk management using artificial intelligence.
Wavelet clustering in time series analysis.
What is the best approximation of ruin probability in infinite time?
We compare 12 different approximations of ruin probability in infinite time studying typical light- and heavy-tailed claim size distributions, namely exponential, mixture of exponentials, gamma, lognormal, Weibull, loggamma, Pareto and Burr. We show that approximation based on the Pollaczek-Khinchin formula gives most accurate results, in fact it can be chosen as a reference method. We also introduce a promising modification to the De Vylder approximation.
When inflation causes no increase in claim amounts.
Zur Theorie des mittleren Risikos der ferneren Dauer von Versicherungen mit kontinuierlicher Prämienberechnung, die auf zweiändrigen Ausscheideordnungen beruhen
Zwei versicherungsmathematische Integralgleichungen