arXiv research

Optimal dividend strategy for insurance company in foreign currency.

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…

New model captures insurance risk dependencies efficiently.

The paper analyzes systemic risk in an insurance model with multiple business lines and heterogeneous claims.

This paper models insurance company insolvency using Lévy processes.

This paper presents some new results on Parisian ruin under Levy insurance risk process, where ruin occurs when the process has gone below a fixed level from the last record maximum, also known as the high-water mark or drawdown, for a fixed consecutive periods of time. The law of ruin-time and the position at ruin is …

The paper analyzes insurance risk with Parisian ruin and capital injection.

For the sum process $X=X^1+X^2$ of a bivariate Lévy process $(X^1,X^2)$ with possibly dependent components, we derive a quintuple law describing the first upwards passage event of $X$ over a fixed barrier, caused by a jump, by the joint distribution of five quantities: the time relative to the time of the previous maxi…

In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative Lévy process in the absence of dividend payments. The classical dividend problem for an insurance company consists in finding a dividend payment policy that maximizes the total expected di…

In this note we apply the recently established Wiener-Hopf Monte Carlo (WHMC) simulation technique for Levy processes from Kuznetsov et al. [17] to path functionals, in particular first passage times, overshoots, undershoots and the last maximum before the passage time. Such functionals have many applications, for inst…

In this paper, we investigate Parisian ruin for a Lévy surplus process with an adaptive premium rate, namely a refracted Lévy process. More general Parisian boundary-crossing problems with a deterministic implementation delay are also considered. Our main contribution is a generalization of the result in Loeffen et al.…

In this paper, we introduce the concept of \emph{Poissonian occupation times} below level $0$ of spectrally negative Lévy processes. In this case, occupation time is accumulated only when the process is observed to be negative at arrival epochs of an independent Poisson process. Our results extend some well known conti…

In this paper we analyze so-called Parisian ruin probability that happens when surplus process stays below zero longer than fixed amount of time $ζ>0$. We focus on general spectrally negative Lévy insurance risk process. For this class of processes we identify expression for ruin probability in terms of some other quan…

In this paper we consider two problems on optimal implementation delay of taxation with trade-off for spectrally negative Lévy insurance risk processes. In the first case, we assume that an insurance company starts to pay tax when its surplus reaches a certain level $b$ and at the termination time of the business there…

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…

In this paper we consider dividend problem for an insurance company whose risk evolves as a spectrally negative Lévy process (in the absence of dividend payments) when Parisian delay is applied. The objective function is given by the cumulative discounted dividends received until the moment of ruin when so-called barri…

The paper develops a valuation framework for GLWB-LTC contracts with Levy dynamics and stochastic interest rates.

In this paper, we introduce an insurance ruin model with adaptive premium rate, thereafter refered to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model, the premium rate is increased as soon as the wealth process falls into the red zone and is brought back to its regul…

In this paper we introduce a new coherent cumulative risk measure on $\mathcal{R}_L^p$, the space of càdlàg processes having Laplace transform. This new coherent risk measure turns out to be tractable enough within a class of models where the aggregate claims is driven by a spectrally positive Lévy process. Moreover, w…

In this note we find a formula for the supremum distribution of spectrally positive or negative Lévy processes with a broken linear drift. This gives formulas for ruin probabilities in the case when two insurance companies (or two branches of the same company) divide between them both claims and premia in some specifie…

The paper finds optimal threshold strategies for insurance companies with a positive terminal value at creeping ruin.

Climate change is widely expected to increase weather related damage and the insurance claims that result from it. This will increase insurance premiums, in a way that is independent of a customer's contribution to the causes of climate change. Insurance provides a financial mechanism that mitigates some of the consequ…

In this paper we consider some insurance policies related to drawdown and drawup events of log-returns for an underlying asset modeled by a spectrally negative geometric Lévy process. We consider four contracts, three of which were introduced in Zhang et al. (2013) for a geometric Brownian motion. The first one is an i…

Parametric insurance offers better risk-sharing in high-risk settings than traditional indemnity insurance.

The study examines how formal index insurance compares to informal risk sharing in managing natural disasters.

Two pension funds mutually insure against longevity risk.

Study on systemic risk in European insurance sector, showing insurer connections during stress.

Develops a Bonus-Malus model for cyber risk insurance to incentivize cybersecurity.

The paper examines how risk reduction and insurance choices interact under convex premium principles.

The paper calculates bonus values in complex insurance schemes.

The paper analyzes how to combine self-protection and self-insurance for risk reduction.

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 on cyber insurance viability using statistical models.

Network theory assesses systemic risk in the insurance sector.

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 …

Algorithmic insurance tackles financial risks from AI errors, proving CVaR-optimal thresholds reduce tail risk.

Study shows subordinated Cramér-Lundberg model increases ruin probability.

Optimal insurance contracts are designed to screen risk preferences and risk types under asymmetric information.

Study proposes a tax-based system to share disaster risk among regions.

This study tackles basis risk in weather parametric insurance using Monte Carlo simulations.

The paper models and prices cyber insurance risks, distinguishing idiosyncratic, systematic, and systemic risks.

This paper discusses the valuation of credit default swaps, where default is announced when the reference asset price has gone below certain level from the last record maximum, also known as the high-water mark or drawdown. We assume that the protection buyer pays premium at fixed rate when the asset price is above a p…

Auto insurers improve risk assessment using t-SNE.

Reinsurance can help life insurers maintain higher capital guarantees without losing utility.

Study optimal reinsurance for insurers with a reinsurer's default risk.

Investment and insurance decisions are studied in a model with nonlinear portfolio frictions and background risk.

Novel convex risk measures aggregate multiple uncertain sources for insurance firms.

Fair insurance contracts are designed to handle default risk using cooperative game theory.