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Risks, Volume 12, Issue 3 (March 2024) – 15 articles

Cover Story (view full-size image): Andrey Andreyevich Markov was a mathematician from Russia who was known for his work on stochastic processes and, eventually, Markov processes. A Markov process lies at the heart of the regime-switching structural default risk model (RSDR) presented in this paper. The RSDR model is essentially a two-state Markov process, where a lognormal distribution lies at each state. The beauty of regime-switching models estimated through maximum likelihood is that it has the flexibility to accommodate any distribution at each state, hence allowing the achievement of multimodality and heavy tails to model periods of elevated volatility and extreme changes in mean returns. These characteristics of regime-switching models are especially useful in periods of market downturns and allow the RSDR model to be more responsive than benchmark models in incorporating new information about the underlying asset. View this paper
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17 pages, 2884 KiB  
Article
Adding Shocks to a Prospective Mortality Model
by Frédéric Planchet and Guillaume Gautier de La Plaine
Risks 2024, 12(3), 57; https://0-doi-org.brum.beds.ac.uk/10.3390/risks12030057 - 20 Mar 2024
Viewed by 742
Abstract
This work proposes a simple model to take into account the annual volatility of the mortality level observed on the scale of a country like France in the construction of prospective mortality tables. By assigning a frailty factor to a basic hazard function, [...] Read more.
This work proposes a simple model to take into account the annual volatility of the mortality level observed on the scale of a country like France in the construction of prospective mortality tables. By assigning a frailty factor to a basic hazard function, we generalise the Lee–Carter model. The impact on prospective life expectancies and capital requirements in the context of a life annuity scheme is analysed in detail. Full article
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24 pages, 1773 KiB  
Article
Exploring Systemic Risk Dynamics in the Chinese Stock Market: A Network Analysis with Risk Transmission Index
by Xiaowei Zeng, Yifan Hu, Chengjun Pan and Yanxi Hou
Risks 2024, 12(3), 56; https://0-doi-org.brum.beds.ac.uk/10.3390/risks12030056 - 20 Mar 2024
Viewed by 732
Abstract
Systemic risk refers to the potential for a disruption in one part of a financial system to trigger a cascade of adverse effects, impacting the functioning of the system. Despite the progress on novel systemic risk measures, research on dynamics of systemic risk [...] Read more.
Systemic risk refers to the potential for a disruption in one part of a financial system to trigger a cascade of adverse effects, impacting the functioning of the system. Despite the progress on novel systemic risk measures, research on dynamics of systemic risk network structure and its community effect is still in its initial state. In this study, we utilize price data from 107 representative Chinese stocks spanning the period from 2017 to 2022. A systemic risk network is derived from the Risk Transmission Index based on TENET and the QR–Lasso model. By utilizing DBSCAN, HITS and community detection algorithms on the network, we aim to propose a more suitable definition of systemically important companies, explore the interrelationships between companies, and discuss its plausible reasons for dynamics structural changes. The empirical findings demonstrate a substantial involvement of insurance companies in both contributing to and receiving systemic risk within the analyzed context. We identify prominent risk output and input centers, and emphasize the profound impact of the COVID-19 pandemic on the dynamics of systemic risk. Full article
(This article belongs to the Special Issue Risk Analysis in Financial Crisis and Stock Market)
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35 pages, 669 KiB  
Article
Capital Structure Models and Contingent Convertible Securities
by Di Meng, Adam Metzler and R. Mark Reesor
Risks 2024, 12(3), 55; https://0-doi-org.brum.beds.ac.uk/10.3390/risks12030055 - 18 Mar 2024
Viewed by 844
Abstract
We implemented a methodology to calibrate capital structure models for banks that have issued contingent convertible securities (CoCos). Typical studies involving capital structure model calibration focus on non-financial firms as they have lower leverage and no contingent convertible securities. From a theoretical perspective, [...] Read more.
We implemented a methodology to calibrate capital structure models for banks that have issued contingent convertible securities (CoCos). Typical studies involving capital structure model calibration focus on non-financial firms as they have lower leverage and no contingent convertible securities. From a theoretical perspective, we found that jumps in the asset value process were necessary to obtain a satisfactory fit to the market data. In practice, contingent capital conversion triggers are discretionary, and there is considerable uncertainty around when regulators are likely to enforce conversion. The market-implied conversion triggers we obtain indicate that the market expects regulators to enforce conversion while the issuing bank is a going concern, as opposed to a gone concern. This fact is presumably of interest to potential dealers, regulators, issuers, and investors. Full article
(This article belongs to the Special Issue Risk Analysis in Financial Crisis and Stock Market)
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16 pages, 931 KiB  
Article
Shareholders in the Driver’s Seat: Unraveling the Impact on Financial Performance in Latvian Fintech Companies
by Ramona Rupeika-Apoga, Stefan Wendt and Victoria Geyfman
Risks 2024, 12(3), 54; https://0-doi-org.brum.beds.ac.uk/10.3390/risks12030054 - 18 Mar 2024
Viewed by 851
Abstract
Fintech companies are relatively young and operate in a rapidly evolving and ever-changing industry, which makes it important to understand how different factors, including shareholder presence in management roles, affect their performance. This study investigates the impact of shareholder presence in director and [...] Read more.
Fintech companies are relatively young and operate in a rapidly evolving and ever-changing industry, which makes it important to understand how different factors, including shareholder presence in management roles, affect their performance. This study investigates the impact of shareholder presence in director and manager positions on the financial performance of Latvian fintechs. Our investigation centers on essential financial ratios, including Return on Assets, Return on Equity, Profit Margin, Liquidity Ratio, Current Ratio, and Solvency Ratio. Our findings suggest that the presence of shareholders in director and manager roles does not significantly affect the financial performance of fintech companies. Although the statistical analysis did not yield significant results, it is important to consider additional insights garnered from Cliff’s Delta effect sizes. Specifically, despite the lack of statistical significance, practical significance indicates that fintech companies in which directors and managers are shareholders show slightly better performance than other fintech companies. Beyond shedding light on the intricacies of corporate governance in the fintech sector, this research serves as a valuable resource for investors, stakeholders, and fellow researchers seeking to understand the impact of shareholder presence in director and manager roles on the financial performance of fintechs. Full article
(This article belongs to the Special Issue Financial Analysis, Corporate Finance and Risk Management)
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24 pages, 1235 KiB  
Article
A Quantitative Comparison of Mortality Models with Jumps: Pre- and Post-COVID Insights on Insurance Pricing
by Şule Şahin and Selin Özen
Risks 2024, 12(3), 53; https://0-doi-org.brum.beds.ac.uk/10.3390/risks12030053 - 14 Mar 2024
Viewed by 783
Abstract
Population events such as natural disasters, pandemics, extreme weather, and wars might cause jumps that have an immediate impact on mortality rates. The recent COVID-19 pandemic has demonstrated that these events should not be treated as nonrepetitive exogenous interventions. Therefore, mortality models incorporating [...] Read more.
Population events such as natural disasters, pandemics, extreme weather, and wars might cause jumps that have an immediate impact on mortality rates. The recent COVID-19 pandemic has demonstrated that these events should not be treated as nonrepetitive exogenous interventions. Therefore, mortality models incorporating jump effects are particularly important to capture the adverse mortality shocks. The mortality models with jumps, which we consider in this study, differ in terms of the duration of the jumps–transitory or permanent–the frequency of the jumps, and the size of the jumps. To illustrate the effect of the jumps, we also consider benchmark mortality models without jump effects, such as the Lee-Carter model, Renshaw and Haberman model and Cairns-Blake-Dowd model. We discuss the performance of all the models by analysing their ability to capture the mortality deterioration caused by COVID-19. We use data from different countries to simulate the mortality rates for the pandemic and post-pandemic years and examine their accuracy in forecasting the mortality jumps due to the pandemic. Moreover, we also examine the jump-free and jump models in terms of their impact on insurance pricing, specifically term annuity and life insurance present values calibrated for both pre- and post-COVID data. Full article
(This article belongs to the Special Issue Extreme Events: Mortality Modelling and Insurance)
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21 pages, 1758 KiB  
Article
Unveiling Outperformance: A Portfolio Analysis of Top AI-Related Stocks against IT Indices and Robotics ETFs
by Ali Trabelsi Karoui, Sonia Sayari, Wael Dammak and Ahmed Jeribi
Risks 2024, 12(3), 52; https://0-doi-org.brum.beds.ac.uk/10.3390/risks12030052 - 13 Mar 2024
Viewed by 1273
Abstract
In this study, we delve into the financial market to compare the performance of prominent AI and robotics-related stocks against traditional IT indices, such as the Nasdaq, and specialized AI and robotics ETFs. We evaluate the role of these stocks in diversifying portfolios, [...] Read more.
In this study, we delve into the financial market to compare the performance of prominent AI and robotics-related stocks against traditional IT indices, such as the Nasdaq, and specialized AI and robotics ETFs. We evaluate the role of these stocks in diversifying portfolios, analyzing their return potential and risk profiles. Our analysis includes various investment scenarios, focusing on common AI-related stocks in the United States. We explore the influence of risk management strategies, ranging from “buy and hold” to daily rebalancing, on AI stock portfolios. This involves investigating long-term strategies like buy and hold, as well as short-term approaches, such as daily rebalancing. Our findings, covering the period from 30 April 2021, to 15 September 2023, show that AI-related stocks have not only outperformed in recent years but also highlight the growing “AI bubble” and the increasing significance of AI in investment decisions. The study reveals that these stocks have delivered superior performance, as indicated by metrics like Sharpe and Treynor ratios, providing insights into market trends and financial returns in the technology and robotics sectors. The results are particularly relevant for investors and traders in the AI sector, offering a balanced view of potential returns against the risks in this rapidly evolving market. This paper adds to the financial market literature by demonstrating that investing in emerging trends, such as AI, can be more advantageous in the short term compared to traditional markets like the Nasdaq. Full article
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20 pages, 1219 KiB  
Article
Assessing Financial Stability in Turbulent Times: A Study of Generalized Autoregressive Conditional Heteroskedasticity-Type Value-at-Risk Model Performance in Thailand’s Transportation Sector during COVID-19
by Danai Likitratcharoen and Lucksuda Suwannamalik
Risks 2024, 12(3), 51; https://0-doi-org.brum.beds.ac.uk/10.3390/risks12030051 - 13 Mar 2024
Viewed by 885
Abstract
The Value-at-Risk (VaR) metric serves as a pivotal tool for quantifying market risk, offering an estimation of potential investment losses. Predominantly employed within financial sectors, it aids in adhering to regulatory mandates and in devising capital reserve strategies. Nonetheless, the predictive precision of [...] Read more.
The Value-at-Risk (VaR) metric serves as a pivotal tool for quantifying market risk, offering an estimation of potential investment losses. Predominantly employed within financial sectors, it aids in adhering to regulatory mandates and in devising capital reserve strategies. Nonetheless, the predictive precision of VaR models frequently faces scrutiny, particularly during crises and heightened uncertainty phases. Phenomena like volatility clustering impinge on the accuracy of these models. To mitigate such constraints, conditional volatility models are integrated to augment the robustness and adaptability of VaR approaches. This study critically evaluates the efficacy of GARCH-type VaR models within the transportation sector amidst the Thai stock market’s volatility during the COVID-19 pandemic. The dataset encompasses daily price fluctuations in the Transportation Sector index (TRANS), the Service Industry index (SERVICE), and 17 pertinent stocks within the Stock Exchange of Thailand, spanning from 28 December 2018 to 28 December 2023, thereby encapsulating the pandemic era. The employed GARCH-type VaR models include GARCH (1,1) VaR, ARMA (1,1)—GARCH (1,1) VaR, GARCH (1,1)—M VaR, IGARCH (1,1) VaR, EWMA VaR, and csGARCH (1,1) VaR. These are juxtaposed with more traditional, less computationally intensive models like the Historical Simulation VaR and Delta Normal VaR. The backtesting methodologies encompass Kupiec’s POF test, the Independence Test, and Christoffersen’s Interval Forecast test. Intriguingly, the findings reveal that the Historical Simulation VaR model surpasses GARCH-type VaR models in failure rate accuracy. Within the GARCH-type category, the EWMA VaR model exhibited superior failure rate accuracy. The csGARCH (1,1) VaR and EWMA VaR models emerged as notably robust. These findings bear significant implications for managerial decision-making in financial risk management. Full article
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23 pages, 7524 KiB  
Article
Value-at-Risk Effectiveness: A High-Frequency Data Approach with Semi-Heavy Tails
by Mario Ivan Contreras-Valdez, Sonal Sahu, José Antonio Núñez-Mora and Roberto Joaquín Santillán-Salgado
Risks 2024, 12(3), 50; https://0-doi-org.brum.beds.ac.uk/10.3390/risks12030050 - 13 Mar 2024
Viewed by 887
Abstract
In the broader landscape of cryptocurrency risk management, this study delves into the nuanced estimation of Value-at-Risk (VaR) for a uniformly weighted portfolio of cryptocurrencies, employing the bivariate Normal Inverse Gaussian distribution renowned for its semi-heavy tails. Utilizing high-frequency data spanning between 1 [...] Read more.
In the broader landscape of cryptocurrency risk management, this study delves into the nuanced estimation of Value-at-Risk (VaR) for a uniformly weighted portfolio of cryptocurrencies, employing the bivariate Normal Inverse Gaussian distribution renowned for its semi-heavy tails. Utilizing high-frequency data spanning between 1 January 2017 and 25 October 2022, with a primary focus on Bitcoin and Ethereum, our research seeks to accentuate the resilience of VaR methodology as a paramount risk assessment tool. The essence of our investigation lies in advancing the comprehension of VaR accuracy by quantitatively comparing the observed returns of both cryptocurrencies with their corresponding estimated values, with a central theme being the endorsement of the Normal Inverse Gaussian distribution as a potent model for risk measurement, particularly in the domain of high-frequency data. To bolster the statistical reliability of our results, we adopt a forward test methodology, showcasing not only a contribution to the evolution of risk assessment techniques in Finance but also underscoring the practicality of sophisticated distributional models in econometrics. Our findings not only contribute to the refinement of risk assessment methods but also highlight the applicability of such models in precisely modeling and forecasting financial risk within the dynamic realm of cryptocurrencies, epitomized by the case study of Bitcoin and Ethereum. Full article
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17 pages, 469 KiB  
Article
The Role of Longevity-Indexed Bond in Risk Management of Aggregated Defined Benefit Pension Scheme
by Xiaoyi Zhang, Yanan Li and Junyi Guo
Risks 2024, 12(3), 49; https://0-doi-org.brum.beds.ac.uk/10.3390/risks12030049 - 06 Mar 2024
Viewed by 871
Abstract
Defined benefit (DB) pension plans are a primary type of pension schemes with the sponsor assuming most of the risks. Longevity-indexed bonds have been used to hedge or transfer risks in pension plans. Our objective is to study an aggregated DB pension plan’s [...] Read more.
Defined benefit (DB) pension plans are a primary type of pension schemes with the sponsor assuming most of the risks. Longevity-indexed bonds have been used to hedge or transfer risks in pension plans. Our objective is to study an aggregated DB pension plan’s optimal risk management problem focusing on minimizing the solvency risk over a finite time horizon and to investigate the investment strategies in a market, comprising a longevity-indexed bond and a risk-free asset, under stochastic nominal interest rates. Using the dynamic programming technique in the stochastic control problem, we obtain the closed-form optimal investment strategy by solving the corresponding Hamilton–Jacobi–Bellman (HJB) equation. In addition, a comparative analysis implicates that longevity-indexed bonds significantly reduce solvency risk compared to zero-coupon bonds, offering a strategic advantage in pension fund management. Besides the closed-form solution and the comparative study, another novelty of this study is the extension of actuarial liability (AL) and normal cost (NC) definitions, and we introduce the risk neutral valuation of liabilities in DB pension scheme with the consideration of mortality rate. Full article
(This article belongs to the Special Issue Optimal Investment and Risk Management)
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33 pages, 5115 KiB  
Article
The Regime-Switching Structural Default Risk Model
by Andreas Milidonis and Kevin Chisholm
Risks 2024, 12(3), 48; https://0-doi-org.brum.beds.ac.uk/10.3390/risks12030048 - 04 Mar 2024
Viewed by 936
Abstract
We develop the regime-switching default risk (RSDR) model as a generalization of Merton’s default risk (MDR) model. The RSDR model supports an expanded range of asset probability density functions. First, we show using simulation that the RSDR model incorporates [...] Read more.
We develop the regime-switching default risk (RSDR) model as a generalization of Merton’s default risk (MDR) model. The RSDR model supports an expanded range of asset probability density functions. First, we show using simulation that the RSDR model incorporates sudden changes in asset values faster than the MDR model. Second, we empirically implement the RSDR, MDR and an extension of the MDR model with changes in drift parameters, using maximum likelihood estimation. Focusing on the period before and after corporate rating downgrades used primarily for investment advice, we find that the RSDR model uses changes in equity mean returns and volatility to produce higher estimated default probabilities, faster, than both benchmark models. Full article
(This article belongs to the Special Issue Risks Journal: A Decade of Advancing Knowledge and Shaping the Future)
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31 pages, 137964 KiB  
Article
What Matters for Comovements among Gold, Bitcoin, CO2, Commodities, VIX and International Stock Markets during the Health, Political and Bank Crises?
by Wajdi Frikha, Azza Béjaoui, Aurelio F. Bariviera and Ahmed Jeribi
Risks 2024, 12(3), 47; https://0-doi-org.brum.beds.ac.uk/10.3390/risks12030047 - 04 Mar 2024
Viewed by 982
Abstract
This paper analyzes the connectedness between gold, wheat, and crude oil futures, Bitcoin, carbon emission futures, and international stock markets in the G7, BRICS, and Gulf regions with the outbreak of exogenous and unexpected shocks related to health, banking, and political crises. To [...] Read more.
This paper analyzes the connectedness between gold, wheat, and crude oil futures, Bitcoin, carbon emission futures, and international stock markets in the G7, BRICS, and Gulf regions with the outbreak of exogenous and unexpected shocks related to health, banking, and political crises. To this end, we use a wavelet-based method on the returns of different assets during the period 2 January 2019, to 21 April 2023. The empirical findings show that the existence of time-varying linkages between markets is well documented and appears stronger during the COVID-19 pandemic. However, it seems to diminish for some associations with the advent of the Russia-Ukraine War. The empirical results also show that investor risk perceptions measured by the VIX are negatively and substantially linked to stock markets in different regions. Other interesting findings emerge from the connectedness analysis with the outbreak of Silicon Valley bankruptcy. In particular, Bitcoin tends to regain its role as a safe-haven asset against some G7 stock markets during the bank crisis. Such findings can provide valuable insights for investors and policymakers concerning the relationship between different markets during different crises. Full article
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16 pages, 1536 KiB  
Article
Navigating Inflation Challenges: AI-Based Portfolio Management Insights
by Tibor Bareith, Tibor Tatay and László Vancsura
Risks 2024, 12(3), 46; https://0-doi-org.brum.beds.ac.uk/10.3390/risks12030046 - 01 Mar 2024
Viewed by 1094
Abstract
After 2010, the consumer price index fell to a low level in the EU. In the euro area, it remained low between 2010 and 2020. The European Central Bank has even had to take action against the emergence of deflation. The situation changed [...] Read more.
After 2010, the consumer price index fell to a low level in the EU. In the euro area, it remained low between 2010 and 2020. The European Central Bank has even had to take action against the emergence of deflation. The situation changed significantly in 2021. Inflation jumped to levels not seen for 40 years in the EU. Our study aims to use artificial intelligence to forecast inflation. We also use artificial intelligence to forecast stock index changes. Based on the forecasts, we propose portfolio reallocation decisions to protect against inflation. The forecasting literature does not address the importance of structural breaks in the time series, which, among other things, can affect both the pattern recognition and prediction capabilities of various machine learning models. The novelty of our study is that we used the Zivot–Andrews unit root test to determine the breakpoints and partitioned the time series into training and testing datasets along these points. We then examined which database partition gives the most accurate prediction. This information can be used to re-balance the portfolio. Two different AI-based prediction algorithms were used (GRU and LSTM), and a hybrid model (LSTM–GRU) was also included to investigate the predictability of inflation. Our results suggest that the average error of the inflation forecast is a quarter of that of the stock market index forecast. Inflation developments have a fundamental impact on equity and government bond returns. If we obtain a reliable estimate of the inflation forecast, we have time to rebalance the portfolio until the inflation shock is incorporated into government bond returns. Our results not only support investment decisions at the national economy level but are also useful in the process of rebalancing international portfolios. Full article
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13 pages, 419 KiB  
Article
Robust Estimation of the Tail Index of a Single Parameter Pareto Distribution from Grouped Data
by Chudamani Poudyal
Risks 2024, 12(3), 45; https://0-doi-org.brum.beds.ac.uk/10.3390/risks12030045 - 01 Mar 2024
Viewed by 894
Abstract
Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to a MLE become significantly limited when dealing with grouped loss severity data, with [...] Read more.
Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to a MLE become significantly limited when dealing with grouped loss severity data, with only a handful of methods, like least squares, minimum Hellinger distance, and optimal bounded influence function, available. This paper introduces a novel robust estimation technique, the Method of Truncated Moments (MTuM), pecifically designed to estimate the tail index of a Pareto distribution from grouped data. Inferential justification of the MTuM is established by employing the central limit theorem and validating it through a comprehensive simulation study. Full article
(This article belongs to the Special Issue Advancements in Actuarial Mathematics and Risk Theory)
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16 pages, 2151 KiB  
Article
Market Equilibrium and the Cost of Capital with Heterogeneous Investment Horizons
by Moshe Levy and Haim Levy
Risks 2024, 12(3), 44; https://0-doi-org.brum.beds.ac.uk/10.3390/risks12030044 - 29 Feb 2024
Viewed by 908
Abstract
Expected returns, variances, betas, and alphas are all non-linear functions of the investment horizon. This seems to be a fatal conceptual problem for the capital asset pricing model (CAPM), which assumes a unique common horizon for all investors. We show that under the [...] Read more.
Expected returns, variances, betas, and alphas are all non-linear functions of the investment horizon. This seems to be a fatal conceptual problem for the capital asset pricing model (CAPM), which assumes a unique common horizon for all investors. We show that under the standard assumptions, the theoretical CAPM equilibrium surprisingly holds with the 1-period parameters, even when investors have heterogeneous and possibly much longer horizons. This is true not only for risk-averse investors, but for any investors with non-decreasing preferences, including prospect theory investors. Thus, the widespread practice of using monthly betas to estimate the cost of capital is theoretically justified. Full article
(This article belongs to the Special Issue Optimal Investment and Risk Management)
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23 pages, 8949 KiB  
Article
Climate Change-Related Disaster Risk Mitigation through Innovative Insurance Mechanism: A System Dynamics Model Application for a Case Study in Latvia
by Maksims Feofilovs, Andrea Jonathan Pagano, Emanuele Vannucci, Marina Spiotta and Francesco Romagnoli
Risks 2024, 12(3), 43; https://0-doi-org.brum.beds.ac.uk/10.3390/risks12030043 - 28 Feb 2024
Viewed by 1452
Abstract
This study explores how the System Dynamics modeling approach can help deal with the problem of conventional insurance mechanisms by studying the feedback loops governing complex systems connected to the disaster insurance mechanism. Instead of addressing the disaster’s underlying risk, the traditional disaster [...] Read more.
This study explores how the System Dynamics modeling approach can help deal with the problem of conventional insurance mechanisms by studying the feedback loops governing complex systems connected to the disaster insurance mechanism. Instead of addressing the disaster’s underlying risk, the traditional disaster insurance strategy largely focuses on providing financial security for asset recovery after a disaster. This constraint becomes especially concerning as the threat of climate-related disasters grows since it may result in rising long-term damage expenditures. A new insurance mechanism is suggested as a solution to this problem to lower damage costs while safeguarding insured assets and luring new assets to be protected. A local case study utilizing a System Dynamics stock and flow model is created and validated by examining the model’s structure, sensitivity analysis, and extreme value test. The results of the case study performed on a city in Latvia highlight the significance of effective disaster risk reduction strategies applied within the innovative insurance mechanism in lowering overall disaster costs. The logical coherence seen throughout the analysis of simulated scenario results strengthens the established model’s plausibility. The case study’s findings support the innovative insurance mechanism’s dynamic hypothesis and show the main influencing factors on the dynamics within the proposed innovative insurance mechanism. The information this study can help insurance firms, policy planners, and disaster risk managers make decisions that will benefit local communities and other stakeholders regarding climate-related disaster risk mitigation. Full article
(This article belongs to the Special Issue Advancements in Actuarial Mathematics and Insurance Risk Management)
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