Proves Gerber statistic is always non-negative.
problem Verifying the positive semi-definiteness of Gerber statistic.
method Analytical proof of both forms of Gerber statistic.
result Gerber statistic is positive semi-definite.
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48 results for “Gerber statistic”
Review of Gerber-Shiu function for practical actuarial science.
problem Difficulty in numerical approximation and statistical inference of Gerber-Shiu function.
method Comprehensive review of formulations, surplus processes, numerical methods, and statistical inference.
result Enhanced understanding and practical guide for Gerber-Shiu function.
New method uses PINNs to efficiently compute Gerber-Shiu functions.
problem Calculating the Gerber-Shiu function efficiently.
method Physics-informed neural networks (PINNs) embedded with differential equations.
result Demonstrates good performance in approximating Gerber-Shiu functions.
Complementing existing results on minimal ruin probabilities, we minimize expected discounted penalty functions (or Gerber-Shiu functions) in a Cramer-Lundberg model by choosing optimal reinsurance. Reinsurance strategies are modelled as time dependant control functions, which leads to a setting from the theory of opti…
The Gerber-Shiu function provides a way of measuring the risk of an insurance company. It is given by the expected value of a function that depends on the ruin time, the deficit at ruin, and the surplus prior to ruin. Its computation requires the evaluation of the overshoot/undershoot distributions of the surplus proce…
Study analyzes household capital risk and poverty trapping, deriving a new function for capital deficit distribution.
problem Analyzing the risk of household capital falling into poverty.
method Introduced a new Gerber-Shiu function to model trapping time and capital deficit distribution.
result Derived a model for capital deficit distribution at trapping using GB distributions.
Study improves portfolio risk estimation methods using robust covariance and CVaR constraints.
problem Improving portfolio risk estimation in the presence of financial data noise and extreme market conditions.
method Exploration of robust covariance estimators, application of CVaR constraints, use of K-means clustering in optimization.
result Robust covariance estimators can outperform market-weighted benchmarks, especially during bull markets.
Optimal reinsurance strategy found to minimize financial risk.
problem Minimizing financial risk in insurance companies through optimal reinsurance.
method Solving the problem via neural networks and a Cramér-Lundberg model.
result Optimal reinsurance strategy found to control terminal wealth and ruin probability.
Generalized Expected Discounted Penalty Function at General Drawdown for Lévy Risk Processesq-fin.PR
This paper considers an insurance surplus process modeled by a spectrally negative Lévy process. Instead of the time of ruin in the traditional setting, we apply the time of drawdown as the risk indicator in this paper. We study the joint distribution of the time of drawdown, the running maximum at drawdown, the last m…
This paper concerns an optimal dividend distribution problem for an insurance company whose risk process evolves as a spectrally negative Lévy process (in the absence of dividend payments). The management of the company is assumed to control timing and size of dividend payments. The objective is to maximize the sum of …
In this paper, we propose the discrete time Compound Beta-Binomial Risk Model with by-claims, delayed by-claims and randomized dividends. We then analyze the Gerber-Shiu function for the cases where the dividend threshold and under the assumption that the constant discount rate . More specifical…
Improved covariance matrix estimation for portfolio optimization with guaranteed PSD and controlled conditioning.
problem Guaranteeing positive semidefinite ness and controlling spectral conditioning in IQ estimators.
method Introducing squeezing identity and atomic-IQ parameterization to construct structured channel matrices with PSD guarantees and analytic eigen floor for conditioning control.
result Atomic-IQ improves Sharpe ratios and delivers a more stable risk profile compared to standard estimators.
We consider in this paper a general two-sided jump-diffusion risk model that allows for risky investments as well as for correlation between the two Brownian motions driving insurance risk and investment return. We first introduce the model and then find the integro-differential equations satisfied by the Gerber-Shiu f…
This paper stidies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the first passage times and undershoot (overshoot) are obtained. As applications, we pr…
The paper prices weather contracts using a complex temperature model.
problem Accurate pricing of weather contracts under temperature dynamics.
method Time-changed Levy model with mean-reverting dynamics, Fourier expansion, Esscher transform.
result An accurate approximation of weather contract prices.
This paper concerns an optimal dividend distribution problem for an insurance company with surplus-dependent premium. In the absence of dividend payments, such a risk process is a particular case of so-called piecewise deterministic Markov processes. The control mechanism chooses the size of dividend payments. The obje…
Omega risk model with taxq-fin.RM
In this paper we study the Omega risk model with surplus-dependent tax payments in a time-homogeneous diffusion setting. The new model incorporates practical features from both the Omega risk model(Albrecher and Gerber and Shiu (2011)) and the risk model with tax(Albrecher and Hipp (2007)). We explicitly characterize t…
The purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed level of a Levy process and the solution of Gerber and Shiu [Astin Bull. 24 (1994) 195-220], Boyarchenko and Levendorskii […
This paper optimizes periodic dividend strategies for Lévy processes with transaction costs.
problem Maximizing dividends for spectrally negative Lévy processes with fixed transaction costs.
method Using periodic strategies and fixed transaction costs, the paper calculates the value function and shows optimality conditions.
result A sufficient condition for optimality is that the Lévy measure is completely monotonic.
In this paper we study the stochastic area swept by a regular time-homogeneous diffusion till a stopping time. This unifies some recent literature in this area. Through stochastic time change we establish a link between the stochastic area and the stopping time of another associated time-homogeneous diffusion. Then we …
On the surplus management of funds with assets and liabilities in presence of solvency requirementsmath.OC
The paper optimizes dividend strategies for companies with assets and liabilities under solvency constraints.
problem Maximizing dividends while adhering to solvency requirements in the face of correlated asset and liability movements.
method Developed verification lemmas to show optimal barrier dividend strategies in two cases: with and without shareholder funding.
result Optimal dividend strategies are barrier-type, derived in closed form and illustrated.
This paper models insurance company insolvency using Lévy processes.
problem Imitating real-world liquidation process in insurance companies.
method Three-barrier model with spectrally negative Lévy processes.
result Rigorous definition and semi-explicit expressions for liquidation ruin.
We study lightlike submanifolds of indefinite statistical manifolds. Contrary to the classical theory of submanifolds of statistical manifolds, lightlike submanifolds of indefinite statistical manifolds need not to be statistical submanifold. Therefore we obtain some conditions for a lightlike submanifold of indefinite…
Kenmotsu geometry is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In this article, we study the statistical counterpart of a Kenmotsu manifold, that is, Kenmotsu statistical manifold with some related examples. We investigate some statistical curvature properti…
Study anti-invariant submersions from holomorphic statistical manifolds.
problem Understanding submersions in statistical manifolds.
method Introduced and analyzed anti-invariant holomorphic statistical submersions.
result Supported results with examples.
Unified approach to private statistics from empirical to population data.
problem Divided focus on empirical vs population statistics in private statistics.
method Unified methods for both types of statistics.
result Methods for empirical statistics can be applied to population statistics.
The paper introduces a statistical version of contact CR-product for Sasakian statistical manifolds.
problem Characterizing geometric properties of contact CR-submanifolds in Sasakian statistical manifolds.
method Characterization of integrability of invariant and anti-invariant distributions, development of results on specific types of contact CR submanifolds, introduction of statistical contact CR-product.
result Introduction of a statistical version of contact CR-product for Sasakian statistical manifolds.
The Bonnet theorem is proven for statistical manifolds.
problem Locally embeddable statistical manifolds in flat spaces.
method Using statistical embedding and the Gauss--Codazzi--Ricci equations.
result Statistical manifolds with specific tensor properties are locally embeddable to flat statistical manifolds.
Enhances power of covariance matrix tests for high-dimensional data.
problem Testing large covariance matrices in high-dimensional data.
method Proposes a new Fisher's combined probability test for quadratic form and maximum form statistics.
result Boosts power against more general alternatives.
This paper simplifies computing higher-order -statistics efficiently.
problem The inefficiency of computing higher-order -statistics in practice.
method Decomposition, connection to Einstein summation, and treewidth-based complexity estimate.
result A new, more efficient algorithm to compute -statistics.
This paper studies the geometry of immersions into statistical manifolds. A necessary and sufficient condition is obtained for statistical manifold structures to be dual to each other for a non-degenerate equiaffine immersion. Then we obtain conditions for realizing an n-dimensional statistical manifold in an (n+1)-dim…
This work uses statistical mechanics to explain AI learning.
problem Understanding the statistical principles behind AI learning.
method Starting from sample concentration behaviors, the study applies statistical mechanics principles to AI and machine learning.
result Exponential families and statistical quantities are key in AI and machine learning.
The differential geometry of Kenmotsu manifold is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In fact, its statistical counterpart, that is, Kenmotsu statistical manifold also has same importance as that of Kenmotsu manifold. Theoretical physicists have also b…
Author presents the second variational formula for statistical biharmonic maps.
problem Developing a formula for statistical biharmonic maps.
method Introduced the second variational formula for the statistical bi-energy functional.
result The second variational formula can be represented using Hessian curvature in Hessian manifolds.
Study CR-statistical submanifolds in holomorphic statistical spaces.
problem Characterize CR-statistical submanifolds and their properties.
method Optimization technique to relate Ricci curvature and mean curvature.
result Established relationship between Ricci curvature and mean curvature.
New statistics are introduced that maintain the Fisher metric structure closely, akin to sufficient statistics.
problem Maintaining the Fisher metric structure in statistical models.
method Characterizing statistics that maintain the Fisher metric structure bi-Lipschitz equivalently.
result Characterized statistics that preserve the Fisher metric structure closely.
Lightlike hypersurfaces of a statistical manifold are studied. It is shown that a lightlike hypersurface of a statistical manifold is not a statistical manifold with respect to the induced connections, but the screen distribution has a canonical statistical structure. Some relations between induced geometric objects wi…
This paper deals with the applications of an optimization method on submanifolds, that is, geometric inequalities can be considered as optimization problems. In this regard, we obtain optimal Casorati inequalities and Chen-Ricci inequality for a statistical submanifold in a statistical warped product manifold of type $…
New statistical manifolds derived from identity map biharmonicity.
problem Deriving new statistical manifolds from identity map biharmonicity.
method Statistical biharmonicity of identity maps, semi-equiaffine condition, constant curvature.
result Determined statistical structures of new class of manifolds.
Active inference framework improves -statistic estimation efficiency.
problem Costly acquisition of labels for -statistics.
method Active inference framework with optimal sampling rule.
result Substantial gains in estimation efficiency over baseline methods.
Sharp inequalities and solitons studied in statistical submersions.
problem Understanding geometric properties of statistical submersions.
method Proving sharp inequalities and establishing geometrical properties of statistical submersions.
result Characterization of fibers as Ricci-Bourguignon solitons with conformal vector field.
Survey of statistical queries and their applications.
problem Understanding statistical queries and their applications.
method Exploration of statistical queries model, definitions, and connections to learnability.
result Connections to learnability and applications in optimization, evolvability, and differential privacy.
Paper discusses the Fisher metric and differentiability in statistical models.
problem Understanding the relationship between Fisher metric and differentiability in statistical models.
method Comparison of different concepts and models in Information Geometry, mathematical statistics, and measure theory.
result Discussion of various models and their differentiability properties.
Study on lightlike geometry in indefinite Sasakian statistical manifolds.
problem Exploring lightlike hypersurfaces and their properties in indefinite Sasakian statistical manifolds.
method Introducing indefinite Sasakian statistical manifolds and analyzing lightlike hypersurfaces with respect to dual connections.
result An invariant lightlike submanifold of an indefinite Sasakian statistical manifold is itself an indefinite Sasakian statistical manifold.
The paper derives Chen inequalities for statistical submanifolds in cosymplectic manifolds.
problem Deriving Chen inequalities for statistical submanifolds in cosymplectic manifolds.
method Analyzing statistical cosymplectic manifolds and Legendrian submanifolds to derive Chen inequalities.
result Chen inequalities for statistical submanifolds in cosymplectic manifolds and Legendrian submanifolds are derived.
One- and two-sample nonparametric tests for the signal-to-noise ratio based on record statisticsstat.ME
A new family of nonparametric statistics, the r-statistics, is introduced. It consists of counting the number of records of the cumulative sum of the sample. The single-sample r-statistic is almost as powerful as Student's t-statistic for Gaussian and uniformly distributed variables, and more powerful than the sign and…
Almost product structures on statistical manifolds and para-Kähler-like statistical submersionsmath.DG
The main purpose of the present work is to investigate statistical manifolds endowed with almost product structures. We prove that the statistical structure of a para-Kähler-like statistical manifold of constant curvature in the Kurose's sense is a Hessian structure. We also derive the main properties of statistical su…
Investigates transfer learning in spatial statistics.
problem Applying transfer learning to spatial statistics.
method Simple MLP models for spatial data.
result Potential of transfer learning in spatial statistics.