arXiv research

The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the collective risk model, where the total claim size in a portfolio is the sum of a …

A new method for modeling insurance claim frequencies using random proportions.

The paper examines stochastic inequalities involving minimum and maximum claim amounts.

The completeness of a bond market model with infinite number of sources of randomness on a finite time interval in the Heath-Jarrow-Morton framework is studied. It is proved that the market is not complete. A construction of a bounded contingent claim, which can not be replicated, is provided.

We consider two risk-averse financial agents who negotiate the price of an illiquid indivisible contingent claim in an incomplete semimartingale market environment. Under the assumption that the agents are exponential utility maximizers with non-traded random endowments, we provide necessary and sufficient conditions f…

This paper addresses the identification of insurance models with multidimensional screening where insurees have private information about their risk and risk aversion. The model includes a random damage and the possibility of several claims. Screening of insurees relies on their certainty equivalence. The paper then in…

Study optimal hedging for claims with random weights in discrete time.

We consider the problem of hedging a European interest rate contingent claim with a portfolio of zero-coupon bonds and show that an HJM type Markovian model driven by an infinite number of sources of randomness does not have some of the shortcomings found in the classical finite-factor models. Indeed, under natural con…

Study tackles imbalanced data in car insurance claims prediction.

Two machine learning models detect anomalies in ER claims, saving up to 40% in improper payments.

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 $d=0$ and $d>0$ under the assumption that the constant discount rate $ν\in (0,1)$. More specifical…

The completeness problem of the bond market model with the random factors determined by a Wiener process and Poisson random measure is studied. Hedging portfolios use bonds with maturities in a countable, dense subset of a finite time interval. It is shown that under natural assumptions the market is not complete unles…

The paper examines how insurers can select claims for fraud investigation, proposing a randomized approach.

This study compares the largest claims from two insurance portfolios using stochastic orderings.

The paper proves a distribution claim for neural network Jacobians.

This article focuses on the mathematical problem of existence and uniqueness of BSDE with a random terminal time which is a general random variable but not a stopping time, as it has been usually the case in the previous literature of BSDE with random terminal time. The main motivation of this work is a financial or ac…

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 condition…

We establish the duality-formula for the superreplication price in a setting of volatility uncertainty which includes the example of "random G-expectation." In contrast to previous results, the contingent claim is not assumed to be quasi-continuous.

This paper studies the optimal investment problem with random endowment in an inventory-based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers prefe…

Optimizes insurance processing capacity to minimize costs.

Paper studies second order tail probabilities in risk models.

The paper studies a new type of stochastic differential equations for financial claims.

The paper introduces BCART models for aggregate claim amount, improving frequency-severity and joint modeling.

In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by Föllmer, Schied (2002). The dynamic optimization problem of finding a self-financing strategy that minimizes the …

In this work, we focus on fine-tuning an OpenAI GPT-2 pre-trained model for generating patent claims. GPT-2 has demonstrated impressive efficacy of pre-trained language models on various tasks, particularly coherent text generation. Patent claim language itself has rarely been explored in the past and poses a unique ch…

Let $X_{λ_1},\ldots,X_{λ_n}$ be a set of dependent and non-negative random variables share a survival copula and let $Y_i= I_{p_i}X_{λ_i}$, $i=1,\ldots,n$, where $I_{p_1},\ldots,I_{p_n}$ be independent Bernoulli random variables independent of $X_{λ_i}$'s, with ${\rm E}[I_{p_i}]=p_i$, $i=1,\ldots,n$. In actuarial scie…

Let $X_{λ_1},\ldots,X_{λ_n}$ be dependent non-negative random variables and $Y_i=I_{p_i} X_{λ_i}$, $i=1,\ldots,n$, where $I_{p_1},\ldots,I_{p_n}$ are independent Bernoulli random variables independent of $X_{λ_i}$'s, with ${\rm E}[I_{p_i}]=p_i$, $i=1,\ldots,n$. In actuarial sciences, $Y_i$ corresponds to the claim amo…

Study stability of contingent claim solutions under probabilistic perturbations.

IDF++ improves integer discrete flows for lossless compression.

We derive a backward and forward nonlinear PDEs that govern the implied volatility of a contingent claim whenever the latter is well-defined. This would include at least any contingent claim written on a positive stock price whose payoff at a possibly random time is convex. We also discuss suitable initial and boundary…

A new method for predicting insurance claims with statistical guarantees.

Study uses SVM to predict weather-induced home insurance claims and losses.

New volume functions for random hyperbolic surfaces link to spectral gaps.

New model bridges pricing and reserving for insurance claims.

SynthETIC simulates insurance claims with customizable features.

Gromov proposed an averaged version of the Dehn function and claimed that in many cases it should be subasymptotic to the Dehn function. Using results on random walks in nilpotent groups, we confirm this claim for most nilpotent groups. In particular, if a nilpotent group satisfies the isoperimetric inequality $δ(l)<Cl…

Financial undertakings often have to deal with liabilities of the form 'non-hedgeable claim size times value of a tradeable asset', e.g. foreign property insurance claims times fx rates. Which strategy to invest in the tradeable asset is risk minimal? We generalize the Gram-Charlier series for the sum of two dependent …

Extends XVA valuation under stochastic volatility, characterizing value processes via mild solutions.

Traditional non-life reserving models largely neglect the vast amount of information collected over the lifetime of a claim. This information includes covariates describing the policy, claim cause as well as the detailed history collected during a claim's development over time. We present the hierarchical reserving mod…

This paper deals with the super-replication of non path-dependent European claims under additional convex constraints on the number of shares held in the portfolio. The corresponding super-replication price of a given claim has been widely studied in the literature and its terminal value, which dominates the claim of i…

The claim experience of the past is a very important information to calculate the fair price of an insurance contract. In a lot of European countries for instance the prices for motor car insurance depend on the number of claims the driver has reported to the insurance company during the last years. Classically these p…

Synthetic telematics dataset created from insurance claims data.

We consider that the price of a firm follows a non linear stochastic delay differential equation. We also assume that any claim value whose value depends on firm value and time follows a non linear stochastic delay differential equation. Using self-financed strategy and replication we are able to derive a Random Partia…

Using Random Matrix Theory one can derive exact relations between the eigenvalue spectrum of the covariance matrix and the eigenvalue spectrum of its estimator (experimentally measured correlation matrix). These relations will be used to analyze a particular case of the correlations in financial series and to show that…

In this paper the utility optimization problem for a general insurance model is studied. The reserve process of the insurance company is described by a stochastic differential equation driven by a Brownian motion and a Poisson random measure, representing the randomness from the financial market and the insurance claim…

Improved Random Forests detect pure interactions better.

The paper develops formulas for hedging and arbitrage in markets with random stopping times.

By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via adapted differentiable processes generated by a controlled ordinary differential …