Related papers: A note on large deviations in life insurance

Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this…

We investigate models of the life annuity insurance when the company invests its reserve into a risky asset with price following a geometric Brownian motion. Our main result is an exact asymptotic of the ruin probabilities for the case of…

Let $\xi_1, \xi_2,\ldots$ be a sequence of independent and identically distributed random variables with zero mean, finite second moment and regularly varying right distribution tail. Motivated by a stop-loss insurance model, we consider a…

We consider a class of tempered subordinators, namely a class of subordinators with one-dimensional marginal tempered distributions which belong to a family studied in [3]. The main contribution in this paper is a non-central moderate…

The probability that the sum of independent, centered, identically distributed, heavy-tailed random variables achieves a very large value is asymptotically equal to the probability that there exists a single summand equalling that value. We…

Distortion (Denneberg 1990) is a well known premium calculation principle for insurance contracts. In this paper, we study sensitivity properties of distortion functionals w.r.t. the assumptions for risk aversion as well as robustness…

The aggregation of individual risks in large credit and insurance portfolios is guided by diversification and the law of large numbers, which formalizes the convergence of sample averages to their means. At the same time, regulatory capital…

We consider the set M_n of all n-truncated power moment sequences of probability measures on [0,1]. We endow this set with the uniform probability. Picking randomly a point in M_n, we show that the upper canonical measure associated with…

We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…

Large deviation theory quantifies the occurence of events that deviate from the average behavior of a system. Such events arise from non-typical trajectories of the dynamics. In this note we derive the time evolution of these rare…

The stability of the financial system is associated with systemic risk factors such as the concurrent default of numerous small obligors. Hence it is of utmost importance to study the mutual dependence of losses for different creditors in…

We prove a law of large numbers for the loss from default and use it for approximating the distribution of the loss from default in large, potentially heterogenous portfolios. The density of the limiting measure is shown to solve a…

The probability minimizing problem of large losses of portfolio in discrete and continuous time models is studied. This gives a generalization of quantile hedging presented in [3].

In this paper, we discuss the ambiguous chance constrained based portfolio optimization problems, in which the perturbations associated with the input parameters are stochastic in nature, but their distributions are not known precisely. We…

We analyze the fluctuation of the loss from default around its large portfolio limit in a class of reduced-form models of correlated firm-by-firm default timing. We prove a weak convergence result for the fluctuation process and use it for…

We prove a full large deviations principle in large time, for a diffusion process with random drift V, which is a centered Gaussian shear flow random field. The large deviations principle is established in a ``quenched'' setting, i.e. is…

The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and…

We often rely on probabilistic measures -- e.g. event probability or expected time -- to characterize systems' safety. However, determining these quantities for extremely low-probability events is generally challenging, as standard safety…

This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…

The Large Deviation Principle is established for stochastic models defined by past-dependent non linear recursions with small noise. In the Markov case we use the result to obtain an explicit expression for the asymptotics of exit time.