Date

2022-12-2

Author

Mert, Özenç Murat

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Insurance markets play an essential role in the economy of the world and its structure requires reinsurance policies due to the growth in populations, extreme (catastrophic) events, political and economical perspectives. In this thesis, stop-loss contracts, one of the reinsurance policy types, are covered for two different contract types: (i) contracts with retention and (ii) contracts with both retention and cap (maximum). This thesis covers two different methodologies, distributional and stochastic behaviors of the claim amounts for the analysis of loss modeling, the costs of insurer and reinsurer, and exposure curves to obtain a fair premium share. Unlike most studies on reinsurance policies, the thesis makes emphasizes the time-dependent and time-influenced structure of claims and gives comprehensive derivations to model claims amounts and to examine the costs of parties and the exposure curves. In the distributional approach, heavy-tailed distributions, specifically, Pareto, Gamma, and Inverse Gamma, are used and the costs of parties and the exposure curves are derived analytically under the selected distributions. Using Monte Carlo simulations and considering the joint analysis of parties' loss ratios, the optimal retention and maximum levels are found and compared with the values minimizing the risks of parties under VaR and CVaR risk measures. In the stochastic modeling approach, in order to express both random and time-dependent mechanisms of the claim amounts, Geometric Brownian Motion with time-varying parameters is used and the costs of parties and the exposure curves are derived analytically since the time elapses during the contract period brings dissimilarities on the claim behavior so does on the cost, premium share. Furthermore, Pareto-Beta stochastic jump diffusion (PBJD) model and its theory are implemented for capturing possible extreme losses. The analytical derivations for the costs and the exposure curves under PBJD are also collected. The emphasis on the applications of real-life data, specifically Turkey's compulsory traffic insurance claims, is made for the stochastic approaches. The results for the expected costs and the exposure curves are presented. In order to obtain the forecasts values of the loss amounts, the expected costs, and the exposure curves, the time-varying parameters are taken as time series and ARIMA family models and cubic spline extrapolation are applied to these series in order to keep the structure of stochastic models.

Subject Keywords

Stop-Loss Reinsurance, Exposure Curves, GBM, PBJD, The Costs of Insurer and Reinsurer, Premium share, ARIMA, Cubic Spline Extrapolation, Forecasting

URI

https://hdl.handle.net/11511/101165

Collections

Graduate School of Applied Mathematics, Thesis