Analytical pricing of time dependent stop-loss reinsurance and exposure curves under time-changed Brownian motion

Date

2026-07-01

Author

Yilmaz, Bilgi
Hekimoglu, Ali Alper
Uğur, Ömür

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

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The risk transfer of insurers to reinsurers is one of the most vital operations in insurance markets. Stop-loss contracts are the most widely adopted contract type for such operations. Specifying the main factors, such as retention and maximum (cap) levels in relation to on random loss, is essential to profit from stop-loss contracts. Thus, this study revisits the stop-loss contract modeling explored by [], where the geometric Brownian motion (GBM) is provided and extends it by using the time-changed Brownian motion, namely, the variance gamma (VG) and normal inverse Gaussian (NIG) processes. The study aims to utilize these processes to model losses and use their advantages of skewness and kurtosis control and calibration. Further, the study illustrates simulations and compares the simulations with the GBM. The numerical experiments show that the VG and NIG processes are promising alternatives to the GBM in modeling the losses.

URI

https://hdl.handle.net/11511/120483

Collections

Graduate School of Applied Mathematics, Article