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Randomly weighted sums of subexponential random variables with application to ruin theory
 Extremes
"... We are interested in the tail behavior of the randomly weighted sum Pn i=1 θiXi, in which the primary random variables X1,..., Xn are real valued, independent and subexponentially distributed, while the random weights θ1,..., θn are nonnegative and arbitrarily dependent, but independent of X1,..., X ..."
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Cited by 15 (4 self)
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We are interested in the tail behavior of the randomly weighted sum Pn i=1 θiXi, in which the primary random variables X1,..., Xn are real valued, independent and subexponentially distributed, while the random weights θ1,..., θn are nonnegative and arbitrarily dependent, but independent of X1,..., Xn. For various cases, we prove that the tail probability of Pn i=1 θiXi is asymptotically equivalent to the sum of the tail probabilities of θ1X1,..., θnXn, which complies with the principle of a single big jump. The results significantly improve the work of Tang and Tsitsiashvili (2003, Extremes). An application to capital allocation is proposed.
Asymptotics for Risk Capital Allocations based on Conditional Tail Expectation
"... Abstract. An investigation of the limiting behavior of a risk capital allocation rule based on the Conditional Tail Expectation (CTE) risk measure is carried out. More specifically, with the help of general notions of Extreme Value Theory (EVT), the aforementioned risk capital allocation is shown to ..."
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Cited by 11 (4 self)
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Abstract. An investigation of the limiting behavior of a risk capital allocation rule based on the Conditional Tail Expectation (CTE) risk measure is carried out. More specifically, with the help of general notions of Extreme Value Theory (EVT), the aforementioned risk capital allocation is shown to be asymptotically proportional to the corresponding ValueatRisk (VaR) risk measure. The existing methodology acquired for VaR can therefore be applied to a somewhat less wellstudied CTE. In the context of interest, the EVT approach is seemingly wellmotivated by modern regulations, which openly strive for the excessive prudence in determining risk capitals.
An overview of comonotonicity and its applications in finance and insurance
, 2010
"... Over the last decade, it has been shown that the concept of comonotonicity is a helpful tool for solving several research and practical problems in the domain of finance and insurance. In this paper, we give an extensive bibliographic overview – without claiming to be complete – of the developments ..."
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Cited by 6 (1 self)
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Over the last decade, it has been shown that the concept of comonotonicity is a helpful tool for solving several research and practical problems in the domain of finance and insurance. In this paper, we give an extensive bibliographic overview – without claiming to be complete – of the developments of the theory of comonotonicity and its applications, with an emphasis on the achievements over the last five years. These applications range from pricing and hedging of derivatives over risk management to life insurance. 1 Comonotonicity Over the last two decades, researchers in economics, financial mathematics and actuarial science have introduced results related to the concept of comonotonicity in their respective fields of interest. In this paper, we give an overview of the relevant literature in these research fields, with the main emphasis on the development of the theory and its applications in finance and insurance over the last five years. Although it is our intention to give an extensive bibliographic overview, due to the high number of papers on applications of comonotonicity, it is impossible to present here an exhaustive overview of the recent literature. Further, we restrict this paper to a description of how and where comonotonicity comes in and refer to the relevant papers for a detailed mathematical description. In order to make this paper selfcontained, we also provide a short overview of the basic definitions and initial main results of comonotonicity theory, hereby referring to part of the older literature on this topic. The concept of comonotonicity is closely related to the following wellknown result, which is usually attributed to both Hoeffding (1940) and Fréchet (1951): For any ndimensional random vector X ≡ (X1, X2,..., Xn) with multivariate cumulative distribution function (cdf) FX and
Asymptotic equivalence of conservative VaR and ESbased capital charges
, 2012
"... We show that the conservative estimate of the ValueatRisk (VaR) for the sum of d random losses with given identical marginals and finite mean is equivalent to the corresponding conservative estimate of the Expected Shortfall (ES), in the limit as d → ∞. Examples of interest in quantitative risk ma ..."
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Cited by 2 (1 self)
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We show that the conservative estimate of the ValueatRisk (VaR) for the sum of d random losses with given identical marginals and finite mean is equivalent to the corresponding conservative estimate of the Expected Shortfall (ES), in the limit as d → ∞. Examples of interest in quantitative risk management show that the equivalence holds also for relatively small risk portfolios. When the random losses Li have infinite first moment, we show that VaR can be arbitrarily large with respect to the corresponding VaR estimate for comonotonic risks if the risk portfolio is large enough.
Capital allocation Conditional Tail Expectation Extreme Value Theory
, 2011
"... Heavytailed distributions ..."
Optimal risk capital under the consideration of systemic risk
"... April 30, 2013Optimal economic capital under the consideration of systemic risk In this article, we discuss the determination of the optimal capital level to be increased under the consideration of systemic risk. We establish several models for calculating optimal capital level to be increased in di ..."
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April 30, 2013Optimal economic capital under the consideration of systemic risk In this article, we discuss the determination of the optimal capital level to be increased under the consideration of systemic risk. We establish several models for calculating optimal capital level to be increased in different conditions including without constraint, with constraints of the value of systemic risk ( SVaR) and the value of expected shortfall of systemic risk ( STVaR) respectively. We also carry out some numerical analysis with the data from 61 main banks of U.S. and Canada. The riskbased capital in general solvency frameworks do not appropriately account for the interdependencies between assets and liabilities of all financial institutions participating in. And the criterion of riskbased capital is determined based on the
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"... This thesis studies the change process of risk management practices associated with the implementation of Enterprise Risk Management (ERM) and the extent to which it can lead to changes in capital allocation practices. The study develops a theoretical framework to study risk management changes, whic ..."
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This thesis studies the change process of risk management practices associated with the implementation of Enterprise Risk Management (ERM) and the extent to which it can lead to changes in capital allocation practices. The study develops a theoretical framework to study risk management changes, which draws on structuration theory (Giddens, 1979, 1984) and institutional theory, particularly the institutional framework of Burns and Scapens (2000), as well as new institutional sociology theory. A twostage empirical study was undertaken in nonlife insurance companies. The first stage was a field study of 10 listed nonlife insurance companies, while the second stage was a case study of a large nonlife insurance company. Multiple data collection methods were used including semistructured interviews, documentary evidence, annual reports, and publicly available data. Findings show internal, coercive, and normative pressures have mainly driven the ERM adoption decision. The literature supports the impact of coercive, mimetic, and normative pressures on the trend toward ERM in financial industries. However, the study finds that internal pressures related to achieving the company's objectives are either equal to or surpass the external pressures. The study also provides empirical evidence of the changes in risk
RISK INDICATORS WITH SEVERAL LINES OF BUSINESS: COMPARISON, ASYMPTOTIC BEHAVIOR AND APPLICATIONS TO OPTIMAL RESERVE ALLOCATION
, 2013
"... Abstract. In a multidimensional risk model with dependent lines of business, we propose to allocate capital with respect to the minimization of some risk indicators. These indicators are sums of expected penalties due to the insolvency of a branch while the global reserve is either positive or nega ..."
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Abstract. In a multidimensional risk model with dependent lines of business, we propose to allocate capital with respect to the minimization of some risk indicators. These indicators are sums of expected penalties due to the insolvency of a branch while the global reserve is either positive or negative. Explicit formulas in the case of two branches are obtained for several models (independent exponential, correlated Pareto). The asymptotic behavior (as the initial capital goes to infinity) is studied. For higher dimension and several periods, no explicit expression is available. Using a stochastic algorithm, we get estimations of the allocation, compare the different allocations and study the impact of dependence.
Tails, Risk Measures, Tail Dependencies and their Influence on Risk Based Capital
"... (Re)insurance companies need to model their liabilities ’ portfolio to compute the riskbased capital (RBC) needed. The RBC depends on both the distribution functions and the dependence functions that are applied. We investigate the impact of those assumptions on an important concept for (re)insuran ..."
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(Re)insurance companies need to model their liabilities ’ portfolio to compute the riskbased capital (RBC) needed. The RBC depends on both the distribution functions and the dependence functions that are applied. We investigate the impact of those assumptions on an important concept for (re)insurance industries: the diversification gain. Several copula models are considered in order to focus on the role of dependencies. To be consistent with the frameworks of both Solvency II and of the Swiss Solvency Test, we deal with two measures of risk: the value at risk and the expected shortfall. We also point out the behavior of different capital allocation principles according both to the assumptions on dependence and to the choice of the risk measure.