Optimal reinsurance minimizes expected discounted penalty in a Cramer-Lundberg model.
problem Minimizing expected discounted penalty functions in a Cramer-Lundberg model.
method Using optimal stochastic control theory and solving the Hamilton-Jacobi-Bellman equation.
result Existence and uniqueness of the solution found by the method.
We consider the problem of maximizing the discounted utility of dividend payments of an insurance company whose reserves are modeled as a classical Cramér-Lundberg risk process. We investigate this optimization problem under the constraint that dividend rate is bounded. We prove that the value function fulfills the Ham…
Study shows subordinated Cramér-Lundberg model increases ruin probability.
problem Analyzing the impact of subordinated time-changed claims on insurance ruin probability.
method Examined a compound Poisson process modified by a Lévy subordinator.
result Probability of ruin decreases slowly with initial capital, despite unchanged total claim amount.
Optimal dividend strategy with ratcheting and capital injection under Cramér-Lundberg model.
problem Optimal dividend payout for an insurance company with ratcheting constraints and capital injections.
method Systematic probabilistic and PDE-based approach to solve HJB equation, constructing strong solution and optimal strategy.
result Existence and uniqueness of strong solution, explicit optimal feedback control strategy.
In this paper, we discuss the Cramér-Lundberg model with investments, where the price of the invested risk asset follows a geometric Brownian motion with drift a and volatility σ>0. By assuming there is a cap on the claim sizes, we prove that the probability of ruin has at least an algebraic decay rate if $2a/σ^2 …
Study examines ruin probability in insurance with stochastic premium and claim arrivals.
problem Analyzing ruin probability in insurance with dependent premium and claim arrivals.
method Adapted Cramer-Lundberg model for mixed Poisson processes with stochastic dependence.
result Explicit expression for ruin probability derived for exponential claim and premium sizes.
Study optimal investment-reinsurance strategy for insurers under random coefficients and jumps.
problem Optimal investment-reinsurance strategy for insurers with random coefficients and jumps.
method Solves backward stochastic differential equations with jumps under a convex cone constraint.
result Optimal strategy and value remain the same even with random coefficients and jumps.
Study optimal investment and reinsurance strategy for insurers under random coefficients.
problem Optimal mean-variance investment-reinsurance problem for insurers under Cramér-Lundberg model with random coefficients.
method Reduced to a constrained stochastic linear-quadratic control problem with jumps, solved using BSDE techniques and SREs.
result Explicit efficient investment-reinsurance strategy and mean-variance frontier.
We analyze the probability of ruin in scaled Cramér-Lundberg risk process and its diffusion approximation.
problem Analyzing the probability of ruin in a scaled Cramér-Lundberg risk process and its diffusion approximation.
method Comparison method to prove convergence of ruin probability and derive the rate of convergence.
result The probability of ruin for the scaled CL process converges to the probability of ruin for the limiting diffusion process with a rate of convergence of order \( \mO\big(n^{-1/2}\big) \) and uniform with respect to surplus.
Study optimal investment strategies for an insurer in two currency markets.
problem Maximizing expected exponential utility of terminal wealth for an insurer in two currency markets.
method Dynamic programming method applied to solve Hamilton-Jacobi-Bellman equations.
result Optimal investment strategies and value functions are derived.
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.
Optimal reinsurance strategy with fixed cost and exponential preferences.
problem Maximizing expected utility of terminal wealth with fixed reinsurance cost.
method Two-step procedure: stochastic control and optimal stopping problem.
result Deterministic optimal strategy depends on model parameters.
Study optimizes insurance investment to maximize utility across all capital levels.
problem Maximizing expected utility across all capital levels in an insurance company's investment strategy.
method Dynamic Programming Principle and Hamilton-Jacobi-Bellman (HJB) equation to prove existence of optimal strategy.
result Existence of optimal investment strategy proven under certain conditions.
An insurer optimizes investment in a market with bank account and risky assets, considering nonlinear economic factors.
problem Optimizing investment strategy for an insurer in a market with bank account and risky assets.
method Adapting dynamic programming approach, deriving Hamilton--Jacobi--Bellman (HJB) equation, proving unique solvability, and solving coupled FBSDEs.
result Derives the optimal investment strategy for an insurer.
Optimizes risk sharing with multiple models under uncertainty.
problem Risk sharing with multiple models under ambiguity.
method Constructs a mean-variance criterion using chi-squared divergence, adapts monotone preferences, and uses dual representation.
result Characterizes optimal risk sharing contract and agent's wealth process.
Study on survival probability of insurance companies using integro-differential equations.
problem Survival probability of insurance companies over infinite time.
method Analytical and numerical methods for solving integro-differential equations with singularities.
result Existence and uniqueness of solutions to the integro-differential equation.
We consider the classical optimal dividends problem under the Cramér-Lundberg model with exponential claim sizes subject to a constraint on the time of ruin. We introduce the dual problem and show that the complementary slackness conditions are satisfied, thus there is no duality gap. Therefore the optimal value functi…
The paper develops new methods to approximate ruin probabilities in a perturbed risk model.
problem Calculating exact ruin probabilities in a perturbed risk model is complex.
method Adapted Cramér-Lundberg model with Wiener process, four approximation methods.
result Four approximation methods provide high accuracy for ruin probabilities.
We consider an insurance company whose surplus is represented by the classical Cramer-Lundberg process. The company can invest its surplus in a risk free asset and in a risky asset, governed by the Black-Scholes equation. There is a constraint that the insurance company can only invest in the risky asset at a limited l…
Paper calculates the distribution of time spent below zero in risk models.
problem Analyzing time spent below zero in risk models.
method Analytical expressions for the distribution of occupation times.
result Improved understanding of risk processes by providing distribution formulas.
We study an optimal investment control problem for an insurance company. The surplus process follows the Cramer-Lundberg process with perturbation of a Brownian motion. The company can invest its surplus into a risk free asset and a Black-Scholes risky asset. The optimization objective is to minimize the probability of…
Investigates optimal reinsurance and investment strategies for insurance companies with stochastic factor effects.
problem Maximizing expected exponential utility of terminal wealth in a stochastic factor model.
method Classical stochastic control approach based on Hamilton-Jacobi-Bellman equation, solving two backward PDEs.
result Characterization of optimal reinsurance-investment strategy and verification of value function.
Study on ruin probabilities for Lévy processes with light-tailed jumps.
problem Determining bounds on ruin probabilities for Lévy processes.
method Analyzing the Laplace exponent of the Lévy process to find bounds on ruin probabilities.
result Identification of a new case not previously considered in the literature.
Study optimizes insurance and investment strategies for risk-averse insurers under ambiguity.
problem Optimizing insurance and investment strategies for risk-averse insurers under ambiguity.
method Solves a coupled FBSDE to derive optimal strategies and value function.
result Optimal consumption, investment, and reinsurance strategies influenced by risk aversion and EIS.
Optimal dividend strategy in insurance with limited rate decrease.
problem Maximizing expected discounted dividends up to ruin in a risk model.
method Two-dimensional optimal control problem solved using Hamilton-Jacobi-Bellman equation.
result Value function is unique viscosity solution and can be approximated by ratcheting strategies.
Study optimal dividend and capital injection in insurance portfolios with self-exciting claim arrivals.
problem Optimal dividend and capital injection in insurance portfolios with Hawkes process claim arrivals.
method Analytical properties, explicit threshold, HJB variational inequality, finite-difference scheme, policy-gradient, actor-critic methods.
result Learned strategies closely match the PDE benchmark and remain stable across initial conditions.
This paper optimizes reinsurance contracts with belief differences between insurer and reinsurer.
problem Dynamic reinsurance design with heterogeneous beliefs under mean-variance framework.
method Modeling surplus process, applying partitioned domain optimization, solving HJB system.
result Optimal reinsurance contracts with belief heterogeneity are more complex than standard contracts.
We consider in this paper the optimal dividend problem for an insurance company whose uncontrolled reserve process evolves as a classical Cramér--Lundberg process. The firm has the option of investing part of the surplus in a Black--Scholes financial market. The objective is to find a strategy consisting of both invest…
A new approach optimizes capital allocation for firms with multiple business lines.
problem Optimizing capital allocation for firms with multiple business lines, especially considering correlations between lines.
method Introducing a common environmental factor, a Bayesian approach to calibrate latent state distribution, and optimal capital determination.
result Developed an easy-to-implement approach for capital risk management in multi-dimensional insurance risk models.
Consider two insurance companies (or two branches of the same company) that receive premiums at different rates and then split the amount they pay in fixed proportions for each claim (for simplicity we assume that they are equal). We model the occurrence of claims according to a Poisson process. The ruin is achieved wh…
Study ruin probabilities in risk processes on stochastic networks.
problem Ruin probabilities in risk processes on stochastic networks.
method Classification of agents by types, Poisson process for loss propagation, explicit ruin probabilities for infinite network size.
result Explicit ruin probabilities for agents of any type in infinite network size.
The field of risk theory has traditionally focused on ruin-related quantities. In particular, the socalled Expected Discounted Penalty Function has been the object of a thorough study over the years. Although interesting in their own right, ruin related quantities do not seem to capture path-dependent properties of the…
Study optimizes CT and microinsurance for efficient social protection in low-income countries.
problem Efficient targeting of cash transfers to reduce social protection costs in low-income countries.
method Modelled household capital dynamics using piecewise-deterministic Markov process, derived HJB equation for optimal injection, used dynamic programming.
result Optimal level of capital injection above poverty threshold for cost-effective social protection.
Study develops time-continuous models and probabilistic descriptions for agent-based economic market models.
problem Formulating and describing agent-based economic market models in a time-continuous and probabilistic manner.
method Derived time-continuous formulations, discussed impact of time-scaling, proved stability, presented probabilistic descriptions using kinetic theory.
result Time-continuous formulations and probabilistic descriptions for agent-based economic market models.
Hybrid model combines interpretable and black-box models for better transparency and performance.
problem Balancing interpretability and predictive performance in machine learning models.
method Proposes a Hybrid Predictive Model (HPM) integrating an interpretable model with a black-box model, using principled objective functions and customized training algorithms.
result Hybrid models achieve an efficient trade-off between transparency and predictive performance.
The paper introduces BCART models for aggregate claim amount, improving frequency-severity and joint modeling.
problem Modeling aggregate claim amount with frequency-severity and joint dependencies.
method Developed three types of BCART models: frequency-severity, sequential, and joint models. Used various distributions for claim severity data.
result Weibull distribution outperforms gamma and lognormal for right-skewed, heavy-tailed claim severity data.
Boosts generative models by combining multiple meta-models.
problem Challenges in creating a single generative model that accurately represents complex data.
method Cascades multiple meta-models (like RBM and VAE) to create a stronger generative model.
result Derives a decomposable variational lower bound for training and evaluating the boosted model.
The paper uses model-based trees to create interpretable surrogate models for complex machine learning models.
problem Interpreting complex machine learning models.
method Using model-based trees to partition feature space and create interpretable models.
result Model-based trees generate optimal surrogate models that balance interpretability and performance.
Study on limits of community detection in various network models.
problem Limits of community detection in network models.
method Analysis of several network models including Stochastic Block Model, Exponential Random Graph Model, Latent Space Model, Directed Preferential Attachment Model, and Directed Small-world Model.
result Information-theoretic limits for recovery of node labels in network models.
Gauge Flow Models use a learnable Gauge Field in Generative Flow Models.
problem Improving generative model performance.
method Integrates a learnable Gauge Field into Flow ODEs.
result Gauge Flow Models outperform traditional Flow Models in Flow Matching experiments.
The study examines how model predictions hold up under model extensions.
problem Model predictions may not be robust under model extensions, limiting their applicability.
method The study uses causal ordering to assess robustness of qualitative model predictions and characterizes model extensions that preserve predictions.
result Conditions and techniques are provided to assess robustness of model predictions under model extensions.
MALC combines interpretable linear models with black-box models for better predictions and transparency.
problem Combining interpretability with black-box models for better predictions.
method Formulates MALC as a convex optimization problem and uses accelerated proximal gradient method for training.
result MALC provides an efficient frontier balancing prediction accuracy and transparency.
Alternative approach to model selection using transformation analysis.
problem Over-simplistic models lead to erroneous interpretations.
method Step-wise complexity reduction to identify simpler, better-interpretable models.
result Transformation models improve model fit and interpretability.
Revises Bayesian model averaging for foundation models.
problem Ensemble pre-trained and lightly-finetuned foundation models for improved classification performance.
method Introduces trainable linear classifiers and computationally cheaper model averaging scheme (OMA).
result Ensembled models can better predict on various datasets.
Paper introduces symmetric divergence link models for probability distributions.
problem Symmetric divergence measures for probability distributions.
method Two general classes of link models: one for survival functions and another for cumulative probability distribution functions.
result Advantages of symmetric divergence measures over asymmetric measures for model averaging and feature assessment.
The paper tests stock return models and uses LSTM to predict stock returns.
problem Validating stock return models and predicting stock returns.
method Used Fama-French three-factor, four-factor, and five-factor models; also used LSTM model.
result Fama-French five-factor model shows better validity for stock returns.
New method to handle credit portfolio model uncertainties.
problem Model risk in credit portfolio models.
method Demonstrates comprehensive yet easy-to-implement approach to uncertainty in model parameters.
result Comprehensive method to deal with model uncertainties.
A new neural network model predicts multi-symbol tokens over multiple scales.
problem Language modeling with improved flexibility and performance.
method A learned dictionary of multi-symbol tokens using BPE compression.
result The model outperforms LSTM on language modeling tasks, especially for smaller models.