ARTICLE | doi:10.20944/preprints201707.0015.v2
Subject: Engineering, Industrial And Manufacturing Engineering Keywords: multi-attribute decision making; reinsurance; proportional reinsurance; non-proportional reinsurance; TOPSIS
Online: 10 July 2017 (15:42:50 CEST)
This article addresses reinsurance decision making process, which involves the insurance company and the reinsurance company, and is negotiated through reinsurance intermediaries. The article proposes a decision flow to model the reinsurance design and selection process. In contrast to existing literature on pure proportional reinsurance or stop-loss reinsurance, this article focuses on the combination into Proportional-Stop-loss reinsurance design which better addresses interest of both parties. In terms of methodology, the significant contribution of the study is to incorporate Multiple Attribute Decision Making (MADM) into modelling the reinsurance selection. The Multi-Objective Decision Making (MODM) model is applied in designing reinsurance alternatives. Then MADM is applied to aid insurance companies in choosing the most appropriate reinsurance contract. To illustrate the feasibility of incorporating intelligent decision supporting system in reinsurance market, the study includes a numerical case study using simulation software @Risk in modeling insurance claims, and programming in MATLAB to realize MADM. Managerial implications could be drawn from the case study results. More specifically, when choosing the most appropriate reinsurance, insurance companies should base their decision on multiple measurements instead of single-criteria decision making models for their decisions to be more robust.
ARTICLE | doi:10.20944/preprints202207.0032.v1
Subject: Computer Science And Mathematics, Probability And Statistics Keywords: twisted Wang transform; shape factor; EP curve; reinsurance; numerical optimization
Online: 4 July 2022 (05:08:29 CEST)
The twisted Wang transform distribution family, defined as the composition of parameter shifted inverse CDF function with an original CDF function, is found to be most suitable for matching low shape factor distributions, characterizing hard to fit or to simulate reinsurance portfolio losses for some perils from our previous study. Among them, the best form for matching a hard-to-fit empirical loss distribution for a specific peril, is the Exponential Fractional Extra Power 0 Distribution in (0,1) with CDF:.The simplest yet still a good form of this family is the Transformed Hyperbolic Tangent Distribution with CDF:,which has analytical formulas for the moments. The twisted Wang transform distribution family is compared and confirmed to be superior to all other well-known distribution families through extensive numerical optimization practice, distribution forms guesses, and computer-aided exploration experiments.
ARTICLE | doi:10.20944/preprints201901.0121.v2
Subject: Computer Science And Mathematics, Applied Mathematics Keywords: ruin probability; jump-diffusion; HJB equation; Volterra equation; block-by-block method; proportional reinsurance; investments
Online: 24 January 2019 (08:52:20 CET)
In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating process and an investment return process. The investment return process is of standard Black-Scholes type, that is, it comprises a single risk-free asset that earns interest at a constant rate and a single risky asset whose price process is modelled by a geometric Brownian motion. Additionally, the company is allowed to purchase noncheap proportional reinsurance priced via the expected value principle. Using the Hamilton-Jacobi-Bellman approach, we derive a second-order Volterra integrodifferential equation which we transform into a linear Volterra integral equation of the second kind. We proceed to solve this integral equation numerically using the block-by-block method for the optimal reinsurance retention level that minimizes the ultimate ruin probability. The numerical results based on light- and heavy-tailed distributions show that proportional reinsurance and investments play a vital role in enhancing the survival of insurance companies. But the ruin probability exhibits sensitivity to the volatility of the stock price.