nep-rmg New Economics Papers
on Risk Management
Issue of 2015‒03‒22
twenty-one papers chosen by



  1. Value-at-Risk in turbulence time By Genest, Benoit; Cao, Zhili
  2. Bounds for randomly shared risk of heavy-tailed loss factors By Oliver Kley; Claudia Kluppelberg
  3. Optimization of Post-Scoring Classification and Impact on Regulatory Capital for Low Default Portfolios By Genest, benoit; Fares, Ziad
  4. Systems and systemic risk in finance and economics By Jean-Pierre Zigrand
  5. The concept of systemic risk By Pawel Smaga
  6. Dynamic Banking with Endogenous Risk Based Funding Cost: Value Maximization, Risk-taking, Responses to Regulation and Credit Contraction By Larsson, Bo; Wijkander, Hans
  7. How insurers differ from banks: a primer on systemic regulation By Christian Thimann
  8. Optimal risk allocation in a market with non-convex preferences By Hirbod Assa
  9. The kiss of information theory that captures systemic risk By Peter Martey Addo; Philippe De Peretti; Hayette Gatfaoui; Jakob Runge
  10. Collateral Optimization : Liquidity & Funding Value Adjustments, - Best Practices - By Genest, Benoit; Rego, David; Freon, Helene
  11. Measuring and managing liquidity risk in the Hungarian practice By Szűcs, Balázs Árpád; Váradi, Kata
  12. Size and Volatility: new evidence from an application of wavelet approach to the emerging Islamic mutual funds’ industry By Alaabed, Alaa; Masih, Mansur
  13. Towards Putting a Price on the Risk of Bank Failure By Daniel Snethlage
  14. A DEA-financial technology: prior to portfolio analysis with DEA By Albane Tarnaud
  15. The effectiveness of index futures hedging in emerging markets during the crisis period of 2008-2010: Evidence from South Africa By Bonga-Bonga, Lumengo; Umoetok, Ekerete
  16. Dynamic Stress Test Diffusion Model Considering the Credit Score Performance By Genest, benoit; Fares, Ziad; Gombert, Arnault
  17. ON Integrated Chance Constraints in ALM for Pension Funds By Youssouf A. F. Toukourou; Fran\c{c}ois Dufresne
  18. Central Counterparty Loss Allocation and Transmission of Financial Stress By Alexandra Heath; Gerard Kelly; Mark Manning
  19. Risk sharing versus risk transfer in Islamic finance: revised By Hasan, Zubair
  20. How to lose money in derivatives: examples from hedge funds and bank trading departments By Bill Ziemba; Sebastien Lleo
  21. Tornadoes and related damage costs: statistical modeling with a semi-Markov approach By Chiara Corini; Guglielmo D'Amico; Filippo Petroni; Flavio Prattico; Raimondo Manca

  1. By: Genest, Benoit; Cao, Zhili
    Abstract: Value-at-Risk (VaR) has been adopted as the cornerstone and common language of risk management by virtually all major financial institutions and regulators. However, this risk measure has failed to warn the market participants during the financial crisis. In this paper, we show this failure may come from the methodology that we use to calculate VaR and not necessarily for VaR measure itself. we compare two different methods for VaR calculation, 1. by assuming the normal distribution of portfolio return, 2. by using a bootstrap method in a nonparametric framework. The Empirical exercise is implemented on CAC40 index, and the results show us that the first method will underestimate the market risk - the failure of VaR measure occurs. Yet, the second method overcomes the shortcomings of the first method and provides results that pass the tests of VaR evaluation.
    Keywords: Value-at-risk, GARCH model, Bootstrap, hit function, VaR evaluation.
    JEL: C0 C1 C5 G1
    Date: 2014–01–27
    URL: http://d.repec.org/n?u=RePEc:pra:mprapa:62906&r=rmg
  2. By: Oliver Kley; Claudia Kluppelberg
    Abstract: For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the agents' exposure risk and the systemic risk in the market. Risk is measured by Value-at-Risk or Conditional Tail Expectation. We assume Pareto tails for the components of $V$ and arbitrary dependence structure in a multivariate regular variation setting. Upper and lower bounds are given by asymptotic independent and fully dependent components of $V$ in dependence of the tail index $\al$ being smaller or larger than 1. Counterexamples complete the picture.
    Date: 2015–03
    URL: http://d.repec.org/n?u=RePEc:arx:papers:1503.03726&r=rmg
  3. By: Genest, benoit; Fares, Ziad
    Abstract: After the crisis of 2008, new regulatory requirements have emerged with supervisors strengthening their position in terms of requirements to meet IRBA standards. Low Default Portfolios (LDP) present specific characteristics that raise challenges for banks when building and implementing credit risk models. In this context, where banks are looking to improve their Return On Equity and supervisors strengthening their positions, this paper aims to provide clues for optimizing Post-Scoring classification as well as analyzing the relationship between the number of classes in a rating scale and the impact on regulatory capital for LDPs.
    Keywords: Basel II, Return On Equity, RWA, Classification trees, Rating scale, Gini, LDP
    JEL: C4 C5 G21
    Date: 2014–04–27
    URL: http://d.repec.org/n?u=RePEc:pra:mprapa:62907&r=rmg
  4. By: Jean-Pierre Zigrand
    Abstract: This paper examines the concept of systemic risk and provides an intuitive account of the economic thought on systems and the development of the notion of systemic risk. It is illustrated by putting the ideas of system, systemic risk and endogenous risk in a historial perspective.
    JEL: G21 G23 G33
    Date: 2014–01–23
    URL: http://d.repec.org/n?u=RePEc:ehl:lserod:61220&r=rmg
  5. By: Pawel Smaga
    Abstract: The aim of the study is to analyze the concept of systemic risk. The study reviews a multitude of systemic risk definitions in the literature. In addition, the paper identifies factors that contribute to the build-up of systemic risk (vulnerabilities), the spreading of contagion and provides a conceptual blueprint linking these phenomena. The author proposes to define systemic risk as the risk that a shock will result in such a significant materialization of (e.g. macrofinancial) imbalances that it will spread on the scale impairing the functioning of financial system and to the extent that it adversely affects the real economy (e.g. economic growth). The blueprint intends to break down and clearly categorize the processes of accumulation, materialization and spreading of systemic risk. This should in turn facilitate its identification and subsequent mitigation by assigning appropriate preventive macroprudential measures. As an example, the blueprint is used to analyze systemic risk stemming from FX lending in CEE countries.
    JEL: J1
    Date: 2014–08–07
    URL: http://d.repec.org/n?u=RePEc:ehl:lserod:61214&r=rmg
  6. By: Larsson, Bo (Dept. of Economics, Stockholm University); Wijkander, Hans (Dept. of Economics, Stockholm University)
    Abstract: We develop a stochastic dynamic model of bank value maximization under limited liability and in which bankruptcy can occur. Main issues are banks’ optimal responses to regulation and credit-losses. We show that risk-neutral banks behave as if they were risk-averse when they are under-capitalized. Risk-taking is always below that of single period value maximization under limited liability. We also show that banking regulations often have significant and adverse second-order effects through banks’ dynamic adjustment to regulations. The model gives rise to endogenous capital buffers and shows that it takes time to re-build bank capital after a credit-loss. That makes the model suitable to analysis of situations as the current post financial crisis period with large macroeconomic disturbances and credit contraction.
    Keywords: Dynamic Banking; Banking regulation; Capital adequacy; Dividends; Incentive structure; Capital buffers; Bankruptcy
    JEL: C61 G21 G22
    Date: 2015–03–09
    URL: http://d.repec.org/n?u=RePEc:hhs:sunrpe:2015_0003&r=rmg
  7. By: Christian Thimann
    Abstract: This paper aims at providing a conceptual distinction between banking and insurance with regard to systemic regulation. It discusses key differences and similarities as to how both sectors interact with the financial system. Insurers interact as financial intermediaries and through financial market investments, but do not share the features of banking that give rise to particular systemic risk in that sector, such as the institutional interconnectedness through the interbank market, the maturity transformation combined with leverage, the prevalence of liquidity risk and the operation of the payment system. The paper also draws attention to three salient features in insurance that need to be taken account in systemic regulation: the quasi-absence of leverage, the fundamentally different role of capital and the ‘built-in bail-in’ of a significant part of insurance liabilities through policy-holder participation. Based on these considerations, the paper argues that if certain activities were to give rise to concerns about systemic risk in the case of insurers, regulatory responses other than capital surcharges may be more appropriate.
    JEL: F3 G3
    Date: 2014–07–23
    URL: http://d.repec.org/n?u=RePEc:ehl:lserod:61218&r=rmg
  8. By: Hirbod Assa
    Abstract: The aims of this study are twofold. First, we consider an optimal risk allocation problem with non-convex preferences. By establishing an infimal representation for distortion risk measures, we give some necessary and sufficient conditions for the existence of optimal and asymptotic optimal allocations. We will show that, similar to a market with convex preferences, in a non-convex framework with distortion risk measures the boundedness of the optimal risk allocation problem depends only on the preferences. Second, we consider the same optimal allocation problem by adding a further assumption that allocations are co-monotone. We characterize the co-monotone optimal risk allocations within which we prove the "marginal risk allocations" take only the values zero or one. Remarkably, we can separate the role of the market preferences and the total risk in our representation.
    Date: 2015–03
    URL: http://d.repec.org/n?u=RePEc:arx:papers:1503.04460&r=rmg
  9. By: Peter Martey Addo (Centre d'Economie de la Sorbonne); Philippe De Peretti (Centre d'Economie de la Sorbonne); Hayette Gatfaoui (NEOMA Business School - Campus de Rouen); Jakob Runge (Postdam Institute for Climate Impact Research and Humboldt University Berlin)
    Abstract: We provide a new approach to understanding systemic risk by analysing complex linkages in finance and insurance sectors. The analysis is achieved by using a recently proposed method for quantifying causal coupling strength, which identifies the existence of causal dependencies between two components of a multivariate time series and assesses the strength of their association by defining a meaningful coupling strength. The measure of association is general, causal and lag-specific, reflecting a well interpretable notion of coupling strength and is pratically computable. A comprehensive analysis of the feasibility of this approach is provided via simulated and real data
    Keywords: Systemic risk, causal dependencies, financial institutions, linkages, Sovereign debt
    JEL: C40 C32 C51 G12 G29
    Date: 2014–10
    URL: http://d.repec.org/n?u=RePEc:mse:cesdoc:14069r&r=rmg
  10. By: Genest, Benoit; Rego, David; Freon, Helene
    Abstract: The purpose of this paper is to understand how the current financial landscape shaped by the crises and new regulations impacts Investment Banking’s business model. We will focus on quantitative implications, i.e. valuation, modeling and pricing issues, as well as qualitative implications, i.e. best practices to manage quantitative aspects and handle these functions to the current Investment Banking organization. We considered two pillars to shape our vision of collateral optimization: 1. Collateral as a refinancing instrument. Collateral is shifting from a mere hedging instrument for counterparty risk to a strategic refinancing instrument. 2. Improve asymmetric collateral quality and profitability. Recent requirements on collateralization highly impact collateral management through the increase in haircuts and funding of good-quality collateral. As a result, more and more banks are considering their net collateral balance as a KPI, i.e. monitoring their net collateral balance position and identifying the need in cash funding or transforming. We built our approach on three key standards: • In most cases, banks should prioritize the reception of cash and delivery of securities, what we call “Asymmetric Collateral Management”. - This implies banks have to capitalize on their valuation functions to boost profitability of the net collateral balance and take advantage of pricing conditions (e.g. for CSA Discounting, precise valuation and pricing of LVA/FVA). • Regarding Management of Non-Cash Collateral, banks should focus on - Optimization of the cash-circuit to manage the various levers of Non-Cash Collateral Transformation into Cash (repo market, central bank loans, re-hypothecation of received non-cash collateral as collateral for other deals). - Management of the collateral quality (both received and delivered), to source and receive high quality collateral and deliver lower quality collateral (Cheapest-To-Deliver Collateral Management). • Considering Management of Liquidity Issues, banks should carefully consider Collateral Management in case of liquidity issues (e.g. sale in case of default, use of re-hypothecation). Being unable to deliver good quality collateral can be seen as a negative sign for the counterparty’s financial health. We will further study the Collateral Offer Services of top financial institutions, providing specific expertise and a tailor-made approach to the new challenges of Collateral Management.
    Keywords: Collateral Management, Collateral Optimization, Collateral Transformation, Liquidity, Funding, Refinancing, Cheapest-to-deliver collateral, Credit Value Adjustment, Debit Value Adjustment, Liquidity Value Adjustment, Funding Value Adjustment, CSA Discounting, OIS Discounting, Collateral Arbitrage
    JEL: G11 G12 G13 G14 G24
    Date: 2013–08–23
    URL: http://d.repec.org/n?u=RePEc:pra:mprapa:62908&r=rmg
  11. By: Szűcs, Balázs Árpád; Váradi, Kata
    Abstract: The crisis that unfolded in 2007/2008 turned the attention of the financial world toward liquidity, the lack of which caused substantial losses. As a result, the need arose for the traditional financial models to be extended with liquidity. Our goal is to discover how Hungarian market players relate to liquidity. Our results are obtained through a series of semistructured interviews, and are hoped to be a starting point for extending the existing models in an appropriate way. Our main results show that different investor groups can be identified along their approaches to liquidity, and they rarely use sophisticated models to measure and manage liquidity. We conclude that although market players would have access to complex liquidity measurement and management tools, there is a limited need for these, because the currently available models are unable to use complex liquidity information effectively.
    Keywords: market liquidity, portfolio optimization, semi-structured interview
    JEL: G11 G32
    Date: 2015
    URL: http://d.repec.org/n?u=RePEc:cvh:coecwp:2015/03&r=rmg
  12. By: Alaabed, Alaa; Masih, Mansur
    Abstract: As far as the author’s knowledge, the paper is the first attempt dedicated to understanding the risk and volatility of constituents of the young and rapidly growing Islamic mutual funds’ industry. The novelty of our approach lies in the usage of wavelet tools to high-frequency financial market data, which allows us to understand the relationship between returns of funds of different sizes in a completely different way. Major part of economic time series analysis is done in time or frequency domain separately. Wavelet analysis can combine these two fundamental approaches, so we can work in time-frequency domain. Using wavelet coherence, we have gained valuable insights into the volatility and continuous dynamics of cross-correlations between small, medium and large size Islamic mutual funds.
    Keywords: Islamic Mutual Funds, Volatility, Size, Assets Under Management, Wavelet Analysis, Wavelet Coherence, Diversification.
    JEL: C22 C58 G2
    Date: 2014–06–15
    URL: http://d.repec.org/n?u=RePEc:pra:mprapa:62991&r=rmg
  13. By: Daniel Snethlage (The Treasury)
    Abstract: This paper develops a new approach for conceptualizing and measuring the risk associated with bank failure. The price of this risk in risk-adjusted present-value terms is estimated at $170-340 million per annum (0.07-0.15% of GDP), representing the price of the financial risk that exists ex-ante (ie, before a bank fails). This can be interpreted as the cost that is either passed onto the banks via higher funding costs, or borne as an implicit risk on the government’s balance sheet. Alternatively, one could think of this as a one-off cost, in the event that all major banks failed in a single crisis. If that were to happen, and if net losses were to be 5-10 per cent of bank liabilities the total cost could be $16-31 billion (7-13% of GDP). This can be interpreted as either the net cost of a government bail-out, or the total value of haircuts on wholesale and retail creditors that would be applied under an Open Bank Resolution (OBR) or a liquidation. Bank bail-outs are not necessarily required or recommended in New Zealand given the existence of OBR. However, the major banks currently receive a one-notch uplift in their credit ratings specifically because of the expectation of government support. These ratings' uplifts are used to estimate the market-implied likelihood that the banks would be bailed out in the event of their failure, and therefore the size of the implicit guarantee banks that are seen to receive. This perceived implicit guarantee is estimated to be worth around $80-$230million per annum (0.04%-0.11% of GDP), equivalent to a 3-8 basis points subsidy on banks' total borrowing costs. This estimate is low by international standards, consistent with the current soundness of the major domestic banks and the relatively low perceived likelihood of government support.
    Keywords: Bank failure; contingent liabilities; implicit guarantee; financial crises; bail-out; bail-in; bank resolution
    JEL: G21 G38 H89
    Date: 2015–03
    URL: http://d.repec.org/n?u=RePEc:nzt:nztwps:15/03&r=rmg
  14. By: Albane Tarnaud (IESEG School of Management (LEM-CNRS); CNRS-LEM and IESEG School of Management)
    Abstract: In this paper, we question the definition of a financial technology that results from the application of a traditional methodology with DEA to the analysis of portfolios of financial assets. We acknowledge the previous applications and show how two approaches have been adopted until now in the literature: a ‘DEA-production’ approach inherited from production theory and a ‘DEA-benchmarking’ approach inherited from operational research. We show how these approaches define the technology regarding financial assets; we also identify which underlying criteria are used for input and output selection. As a basis for a new ‘DEA-financial’ approach, we propose to identify a ‘financial production process’ that differs from the traditional risk-return relationship but is rather based on the generation of a distribution of returns by an initial investment. This identification of a financial production process ensures the proper selection of input and output variables and addresses several issues recently raised by Cook, Tone & Zhu (2014).
    Keywords: Data envelopment analysis; Input; Output; DEA-financial technology; Portfolio
    Date: 2015–03
    URL: http://d.repec.org/n?u=RePEc:ies:wpaper:e201502&r=rmg
  15. By: Bonga-Bonga, Lumengo; Umoetok, Ekerete
    Abstract: This paper provides an assessment of the comparative effectiveness of four econometric methods in estimating the optimal hedge ratio in an emerging equity market, particularly the South African equity and futures markets. The paper bases the effectiveness of hedging on volatility reduction and minimisation of the coefficient of variation of hedged returns as well as risk-aversion based utility maximisation. The empirical analysis shows that the single equation method estimated by ordinary least squares is the most effective over daily hedging periods. However, the vector error-correction method and multivariate GARCH methods are most effective over weekly and monthly hedging periods.
    Keywords: emerging markets, optimal hedge ratio, South Africa, index futures hedging, Vector autoregression, Vector error-correction, GARCH
    JEL: C5 C58 G13
    Date: 2015–03–17
    URL: http://d.repec.org/n?u=RePEc:pra:mprapa:62932&r=rmg
  16. By: Genest, benoit; Fares, Ziad; Gombert, Arnault
    Abstract: After the crisis of 2008, and the important losses and shortfall in capital that it revealed, regulators conducted massive stress testing exercises in order to test the resilience of financial institutions in times of stress conditions. In this context, and considering the impact of these exercises on the banks’ capital, organization and image, this white paper proposes a methodology that diffuses dynamically the stress on the credit rating scale while considering the performance of the credit score. Consequently, the aim is to more accurately reflect the impact of the stress on the portfolio by taking into account the purity of the score and its ability to precisely rank the individuals of the portfolio.
    Keywords: Basel III, Dodd Frank, Stress testing, CCAR, Gini, Rating scale, PD
    JEL: C3 C5 G1
    Date: 2014–01–01
    URL: http://d.repec.org/n?u=RePEc:pra:mprapa:62905&r=rmg
  17. By: Youssouf A. F. Toukourou; Fran\c{c}ois Dufresne
    Abstract: We discuss the role of integrated chance constraints (ICC) as quantitative risk constraints in asset and liability management (ALM) for pension funds. We define two types of ICC: the one period integrated chance constraint (OICC) and the multiperiod integrated chance constraint (MICC). As their names suggest, the OICC covers only one period whereas several periods are taken into account with the MICC. A multistage stochastic linear programming model is therefore developed for this purpose and a special mention is paid to the modeling of the MICC. Based on a numerical example, we firstly analyse the effects of the OICC and the MICC on the optimal decisions (asset allocation and contribution rate) of a pension fund. By definition, the MICC is more restrictive and safer compared to the OICC. Secondly, we quantify this MICC safety increase. The results show that although the optimal decisions from the OICC and the MICC differ, the total costs are very close, showing that the MICC is definitely a better approach since it is more prudent.
    Date: 2015–03
    URL: http://d.repec.org/n?u=RePEc:arx:papers:1503.05343&r=rmg
  18. By: Alexandra Heath (Reserve Bank of Australia); Gerard Kelly (Reserve Bank of Australia); Mark Manning (Reserve Bank of Australia)
    Abstract: Among the reforms to over-the-counter (OTC) derivative markets since the global financial crisis is a commitment to collateralise counterparty exposures and to clear standardised contracts via central counterparties (CCPs). The reforms aim to reduce interconnectedness and improve counterparty risk management in these important markets. At the same time, however, the reforms necessarily concentrate risk in one or a few CCPs and also increase institutions' demand for high-quality assets to meet collateral requirements. This paper looks more closely at the implications of these reforms for the stability of the financial network. Following Heath, Kelly and Manning (2013), the paper examines liquidity and solvency risk under alternative clearing configurations, but extends the analysis in two main ways. First, rather than using simulated data, it uses actual data on the derivative positions of the 41 largest bank participants in global OTC derivative markets in 2012 (as previously used by the Bank for International Settlements' Macroeconomic Assessment Group on Derivatives). Second, it extends the methodolgy to consider in greater depth the implications of loss allocation by CCPs to meet obligations once pre-funded financial resources have been exhausted, and in particular the mechanism of variation margin gains haircutting. This mechanism is considered in international standard-setters' guidance on recovery planning for CCPs and has been adopted by some CCPs. The paper demonstrates that designing and operating CCPs in accordance with international standards can limit the potential for stress to propagate through the system, even in very extreme market conditions.
    Keywords: clearing; netting; financial stability; central counterparty; derivatives; loss allocation; recovery and resolution
    JEL: E42 G17 G23
    Date: 2015–03
    URL: http://d.repec.org/n?u=RePEc:rba:rbardp:rdp2015-02&r=rmg
  19. By: Hasan, Zubair
    Abstract: Some writers on Islamic finance have recently resuscitated the old ‘no risk, no gain’ precept from the earlier literature in the wake of 2007-2008 financial crisis. They argue that the basic reason for the recurrence of such crises is the conventional interest-based financial system that subsists purely on transferring of risks. In contrast, Islam shuns interest and promotes sharing of risks, not their transfer. The distinction is used to make a case for replacing the conventional system with the Islamic; for that alone is thought as the way to ensuring the establishment of a just and stable crisis free financial system. Islamic banks have faced the current crisis better than the conventional is cited as evidence. The present paper is a critique of this line of thought. It argues that risk-sharing is not basic to Islam. It encourages profit sharing of which sharing of risk is a consequence not the cause. The paper concludes that the case is for reform, not for replacement, of the current debt dominated system marked with duality.
    Keywords: Financial crisis; Risk-Sharing; Risk-Transfer; Islamic Banking; KL Declaration
    JEL: B0 G2 G21 G3
    Date: 2014–09
    URL: http://d.repec.org/n?u=RePEc:pra:mprapa:62826&r=rmg
  20. By: Bill Ziemba; Sebastien Lleo
    Abstract: What makes futures hedge funds fail? The common ingredient is over betting and not being diversified in some bad scenarios that can lead to disaster. Once troubles arise, it is difficult to take the necessary actions that eliminate the problem. Moreover, many hedge fund operators tend not to make decisions to minimize losses but rather tend to bet more doubling up hoping to exit the problem with a profit. Incentives, including large fees on gains and minimal penalties for losses, push managers into such risky and reckless behavior. We discuss some specific ways losses occur. To illustrate, we discuss the specific cases of Long Term Capital Management, Niederhoffer’s hedge fund, Amaranth and Société Genéralé. In some cases, the failures lead to contagion in other hedge funds and financial institutions. We also list other hedge fund and bank trading failures with brief comments on them.
    Keywords: hedge fund trading disasters; over betting; Long Term Capital Management; Amarath and Société Genéralé
    JEL: G21 G23 G33
    Date: 2014–05–29
    URL: http://d.repec.org/n?u=RePEc:ehl:lserod:61219&r=rmg
  21. By: Chiara Corini; Guglielmo D'Amico; Filippo Petroni; Flavio Prattico; Raimondo Manca
    Abstract: We propose a statistical approach to tornadoes modeling for predicting and simulating occurrences of tornadoes and accumulated cost distributions over a time interval. This is achieved by modeling the tornadoes intensity, measured with the Fujita scale, as a stochastic process. Since the Fujita scale divides tornadoes intensity into six states, it is possible to model the tornadoes intensity by using Markov and semi-Markov models. We demonstrate that the semi-Markov approach is able to reproduce the duration effect that is detected in tornadoes occurrence. The superiority of the semi-Markov model as compared to the Markov chain model is also affirmed by means of a statistical test of hypothesis. As an application we compute the expected value and the variance of the costs generated by the tornadoes over a given time interval in a given area. he paper contributes to the literature by demonstrating that semi-Markov models represent an effective tool for physical analysis of tornadoes as well as for the estimation of the economic damages to human things.
    Date: 2015–03
    URL: http://d.repec.org/n?u=RePEc:arx:papers:1503.05127&r=rmg

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