Time dependent stop-loss reinsurance and exposure curves

Date

2021-06-01

Author

Mert, Özenç Murat

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

381
views

0
downloads

Stop-loss contracts are the most commonly used reinsurance agreements in insurance whose important factors are the retention and the maximum (cap) values attained on the random loss, which may occur within the policy period. Therefore, determining and forecasting the loss amounts is an important issue for both the insurer and the reinsurer. Along with many approaches in actuarial literature, we propose a geometric Brownian motion (BM) with the time-varying parameters to capture the time-dependent loss amounts. We implement the time-influence on stop-loss contract in the frame of the stochastic model and find the analytical derivations of costs associated with reinsurance contract for reinsurer and insurer with constraints on time, loss amount, retention, and both retention and cap levels. Additionally, the analytical forms of exposure curves are depicted to determine the premium share between reinsurer and insurer under time, loss, retention, and both retention and cap constraints. An application of the proposed methodology on real-life data and the calibration of time-varying parameters using dynamic maximum likelihood estimator and simulations on the proposed model are performed. Finally, we forecast the claim amounts, expected costs, and exposure curves on time-varying parameters using the cubic spline extrapolation and the dynamic ARIMA with trend search. It is shown that the time-varying approach using the stochastic model copes with the behavior of the claims and assures fair share between insurer and reinsurer. (C) 2020 Elsevier B.V. All rights reserved.

Subject Keywords

Stop-loss reinsurance, Geometric Brownian motion, Exposure curves, Dynamic MLE, Dynamic ARIMA

URI

https://hdl.handle.net/11511/89147

Journal

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

DOI

https://doi.org/10.1016/j.cam.2020.113348

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

Optimal premium allocation under stop-loss insurance using exposure curves Mert, Özenç Murat; Kestel, Sevtap Ayşe (2022-1-01) Determining the retention level in the stop-loss insurance risk premium for both insurer and reinsurer is an important factor in pricing. This paper aims to set optimal reinsurance with respect to the joint behavior of the insurer and the reinsurer under stop-loss contracts. The dependence between the costs of insurer and reinsurer is expressed as a function of retention (d) and maximum-cap (m) levels. Based on the maximum degree of correlation, the optimal levels for d and m are derived under certain claim...
Optimal premium allocation under stop-loss insurance using exposure curves Mert, Özenç Murat; Kestel, Sevtap Ayşe (2021-11-01) Determining the retention level in the stop-loss insurance risk premium for both insurer and reinsurer is an important factor in pricing. This paper aims to set optimal reinsurance with respect to the joint behavior of the insurer and the reinsurer under stop-loss contracts. The dependence between the costs of insurer and reinsurer is expressed as a function of retention (d) and maximum-cap (m) levels. Based on the maximum degree of correlation, the optimal levels for d and m are derived under certain claim...
Optimal Premium allocation understop-loss insurance using exposure curves Mert, Özenç Murat; Kestel, Ayşe Sevtap (2022-1-01) Determining the retention level in the stop-loss insurance risk premium for both insurerand reinsurer is an important factor in pricing. This paper aims to set optimal reinsurancewith respect to the joint behavior of the insurer and the reinsurer under stop-loss contracts.The dependence between the costs of insurer and reinsurer is expressed as a function ofretention (d) and maximum-cap (m) levels. Based on the maximum degree of correlation,the optimal levels for d and m are derived under certain claim dist...
Modeling company failure: a longitudinal study of Turkish banks İlk Dağ, Özlem; ÇİNKO, MURAT (2014-01-01) Determining the factors related to the financial failure of a company is important. In this paper, we extend literature on bank failure prediction by modelling bank failures in Turkey from 1998 to 2000 using three statistical models combined with a principal component analysis on financial ratios. The three statistical models employed are a logistic regression, a logistic regression that takes serial correlation into account via generalized estimating equations and a marginalized transition model (MTM). Tim...
Constant proportion portfolio insurance in defined-contribution pension plan management Temoçin, Büşra Zeynep; Kestel, Sevtap Ayşe; Korn, Ralf; Department of Financial Mathematics (2015) In this thesis, various portfolio insurance strategies are designed and proposed for portfolio management of defined-contribution type pension plans. These type of plans consist of consecutive and defined premium payments which are invested in financial markets and lead to a benefit that will be collected at the retirement. Since the beneficiary faces all of the financial risk throughout the plan, a capital protection mechanism is needed in such retirement systems. The main contribution of the present resea...

Citation Formats

Ö. M. Mert, “Time dependent stop-loss reinsurance and exposure curves,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/89147.