scholarly journals COMPETITIVE EQUILIBRIA WITH DISTORTION RISK MEASURES

2015 ◽  
Vol 45 (3) ◽  
pp. 703-728 ◽  
Author(s):  
Tim J. Boonen
Keyword(s):  
Closed Form ◽  
Risk Measures ◽  
Risk Measure ◽  
Insurance Companies ◽  
Pareto Optimal ◽  
Unique Equilibrium ◽  
Insurance Risk ◽  
Solvency Test ◽  
Swiss Solvency Test ◽  
Competitive Equilibria

AbstractThis paper studies optimal risk redistribution between firms, such as banks or insurance companies. The introduction of the Basel II regulation and the Swiss Solvency Test has increased the use of risk measures to evaluate financial or insurance risk. We consider the case where firms use a distortion risk measure (also called dual utility) to evaluate risk. The paper first characterizes all Pareto optimal redistributions. Thereafter, it characterizes all competitive equilibria. It presents three conditions that are jointly sufficient for existence of a unique equilibrium redistribution. This equilibrium's redistribution and prices are provided in closed form via a representative agent.

scholarly journals Geometric-Gamma Collective Modified Value-at-Risk Model in Life Insurance Risk

2018 ◽  
Vol 7 (3.20) ◽  
pp. 372
Author(s):  
Muhammad Iqbal Al-Banna Ismail ◽  
Sukono . ◽  
Abdul Talib BIN Bon ◽  
Yuyun Hidayat ◽  
Eman Lesmana ◽  
...  
Keyword(s):  
At Risk ◽  
Life Insurance ◽  
Value At Risk ◽  
Risk Model ◽  
Risk Measure ◽  
Insurance Companies ◽  
Insurance Company ◽  
Insurance Risk ◽  
Collective Risk Model ◽  
Collective Risk

Claim risk is a payment made by the insurance company to the policyholder. Actuaries in insurance companies should be able to measure and control the risk of claims, in order to avoid losses to insurance companies. In this paper we analyze the Geometric-Gamma Collective Modified Value-at-Risk model in life insurance risk. In this research, there is a development of claim risk measure called Collective Modified Value-at-Risk, which is an extension of Collective Risk model. This Collective Modified Value-at-Risk model requires estimation of the mean, variance, skewness, and kurtosis parameters. The result of this research, is that the extent of this model can be applied to the risk of claims amount of non-normal distributed. Thus, the Collective Modified Value-at-Risk model can serve as one of the statistical alternatives for measuring the risk of claims on life insurance.  

scholarly journals A note on the Swiss Solvency Test risk measure

2008 ◽  
Vol 42 (3) ◽  
pp. 897-902 ◽  
Author(s):  
Damir Filipović ◽  
Nicolas Vogelpoth
Keyword(s):  
Risk Measure ◽  
Solvency Test ◽  
Swiss Solvency Test

scholarly journals RISK REDISTRIBUTION GAMES WITH DUAL UTILITIES

2016 ◽  
Vol 47 (1) ◽  
pp. 303-329 ◽  
Author(s):  
Tim J. Boonen
Keyword(s):  
Institutional Investors ◽  
Competitive Equilibrium ◽  
Risk Measure ◽  
Insurance Companies ◽  
Distortion Risk Measure ◽  
Competitive Equilibria ◽  
Necessary And Sufficient

AbstractThis paper studies optimal risk redistribution between firms, such as institutional investors, banks or insurance companies. We consider the case where every firm uses dual utility (also called a distortion risk measure) to evaluate risk. We characterize optimal risk redistributions via four properties that need to be satisfied jointly. The characterized risk redistribution is unique under three conditions. Whereas we characterize risk redistributions by means of properties, we can also use some results to study competitive equilibria. We characterize uniqueness of the competitive equilibrium in markets with dual utilities. Finally, we identify two conditions that are jointly necessary and sufficient for the case that there exists a trade that is welfare-improving for all firms.

scholarly journals Application of a coherent risk measure in the price calculation of an income insurance (annuities) = Aplicación de una medida de riesgo coherente para el cálculo de la prima de riesgo en un seguro de rentas

2013 ◽  
pp. 41
Author(s):  
Montserrat Hernández Solís ◽  
Emma Berenguer Cárceles
Keyword(s):  
Risk Premium ◽  
Risk Measures ◽  
Risk Measure ◽  
Insurance Coverage ◽  
Distortion Function ◽  
Insurance Companies ◽  
General Level ◽  
Adjusted Risk ◽  
Coherent Risk ◽  
Premium Calculation

<p>Una práctica común que realizan las entidades aseguradoras es la de modificar las tasas de mortalidad instantánea al aplicar el principio de prima neta con el fin de hacer frente a las desviaciones desfavorables de la siniestralidad. Este documento proporciona una respuesta matemática a esta cuestión mediante la aplicación de la función de distorsión de potencia de Wang. Tanto la prima neta y la función de distorsión de Wang son medidas de riesgo coherentes, siendo este último aplicado por primera vez en el campo delos seguros de vida.<br />Utilizando las leyes de Gompertz y Makeham primero calculamos la prima a nivel general y en una segunda parte, se aplica el principio de cálculo de la prima basado en función de distorsión de potencia de Wang para calcular el recargo sobre la prima de riesgo ajustada. El precio de prima única de riesgo se ha aplicado a una forma de cobertura de seguro de supervivencia, el seguro de rentas.La principal conclusión que puede extraerse es que mediante el uso de la función de distorsión, la nueva tasa instantánea de mortalidad es directamente proporcional a un múltiplo, que es justamente el exponente de esta función y hace que el riesgo de longevidad sea mayor. Esta es la razón por la prima de riesgo ajustada es superior a la prima neta.</p><p>Modification of instantaneous mortality rates when applying the net premium principle in order to cope with unfavorable deviations in claims, is common practice carried out by insurance companies. This paper provides a mathematical answer to this matter by applying Wang’s power distortion function. Both net premium and Wang’s distortion function are coherent risk measures, the latter being first applied to the field of life insurance.<br />Using the Gompertz and Makeham laws we first calculate the premium at a general level and in a second part, the principle of premium calculation based on Wang´s power distortion function is applied to calculate the adjusted risk premium surcharge. The risk single premium pricing has been applied to a form of survival insurance coverage called Annuities.The main conclusion to be drawn is that by using the distortion function, the new instantaneous mortality rate is directly proportional to a multiple, which happens to be the exponent of this function and causes longevity risk to be greater. This is why the adjusted risk premium is higher than the net premium.</p>

scholarly journals Immunization Strategies for Funding Multiple Inflation-Linked Retirement Income Benefits

Risks ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 60
Author(s):  
Cláudia Simões ◽  
Luís Oliveira ◽  
Jorge M. Bravo
Keyword(s):  
Interest Rate ◽  
Yield Curve ◽  
Risk Measure ◽  
Management Strategies ◽  
Interest Rate Risk ◽  
Insurance Companies ◽  
Retirement Income ◽  
Investment Strategies ◽  
Immunization Strategies ◽  
The Impact

Protecting against unexpected yield curve, inflation, and longevity shifts are some of the most critical issues institutional and private investors must solve when managing post-retirement income benefits. This paper empirically investigates the performance of alternative immunization strategies for funding targeted multiple liabilities that are fixed in timing but random in size (inflation-linked), i.e., that change stochastically according to consumer price or wage level indexes. The immunization procedure is based on a targeted minimax strategy considering the M-Absolute as the interest rate risk measure. We investigate to what extent the inflation-hedging properties of ILBs in asset liability management strategies targeted to immunize multiple liabilities of random size are superior to that of nominal bonds. We use two alternative datasets comprising daily closing prices for U.S. Treasuries and U.S. inflation-linked bonds from 2000 to 2018. The immunization performance is tested over 3-year and 5-year investment horizons, uses real and not simulated bond data and takes into consideration the impact of transaction costs in the performance of immunization strategies and in the selection of optimal investment strategies. The results show that the multiple liability immunization strategy using inflation-linked bonds outperforms the equivalent strategy using nominal bonds and is robust even in a nearly zero interest rate scenario. These results have important implications in the design and structuring of ALM liability-driven investment strategies, particularly for retirement income providers such as pension schemes or life insurance companies.

scholarly journals Modified Mean-Variance Risk Measures for Long-Term Portfolios

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 111
Author(s):  
Hyungbin Park
Keyword(s):  
Risk Measures ◽  
Risk Measure ◽  
Investment Strategy ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Volatility Model ◽  
Variance Risk ◽  
Investment Portfolios ◽  
Mean Variance

This paper proposes modified mean-variance risk measures for long-term investment portfolios. Two types of portfolios are considered: constant proportion portfolios and increasing amount portfolios. They are widely used in finance for investing assets and developing derivative securities. We compare the long-term behavior of a conventional mean-variance risk measure and a modified one of the two types of portfolios, and we discuss the benefits of the modified measure. Subsequently, an optimal long-term investment strategy is derived. We show that the modified risk measure reflects the investor’s risk aversion on the optimal long-term investment strategy; however, the conventional one does not. Several factor models are discussed as concrete examples: the Black–Scholes model, Kim–Omberg model, Heston model, and 3/2 stochastic volatility model.

scholarly journals Minimizing spectral risk measures applied to Markov decision processes

2021 ◽  
Author(s):  
Nicole Bäuerle ◽  
Alexander Glauner
Keyword(s):  
Minimization Problem ◽  
Risk Measures ◽  
Risk Measure ◽  
Sufficient Conditions ◽  
Planning Horizon ◽  
Insurance Company ◽  
Existence Of A Solution ◽  
Discounted Cost ◽  
Spectral Risk Measures ◽  
Markov Decision

AbstractWe study the minimization of a spectral risk measure of the total discounted cost generated by a Markov Decision Process (MDP) over a finite or infinite planning horizon. The MDP is assumed to have Borel state and action spaces and the cost function may be unbounded above. The optimization problem is split into two minimization problems using an infimum representation for spectral risk measures. We show that the inner minimization problem can be solved as an ordinary MDP on an extended state space and give sufficient conditions under which an optimal policy exists. Regarding the infinite dimensional outer minimization problem, we prove the existence of a solution and derive an algorithm for its numerical approximation. Our results include the findings in Bäuerle and Ott (Math Methods Oper Res 74(3):361–379, 2011) in the special case that the risk measure is Expected Shortfall. As an application, we present a dynamic extension of the classical static optimal reinsurance problem, where an insurance company minimizes its cost of capital.

scholarly journals Portfolio Optimization Constrained by Performance Attribution

2021 ◽  
Vol 14 (5) ◽  
pp. 201
Author(s):  
Yuan Hu ◽  
W. Brent Lindquist ◽  
Svetlozar T. Rachev
Keyword(s):  
Portfolio Optimization ◽  
Asset Allocation ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Selection Effect ◽  
Conditional Value At Risk ◽  
Positive Role ◽  
Performance Attribution ◽  
Dow Jones Industrial Average

This paper investigates performance attribution measures as a basis for constraining portfolio optimization. We employ optimizations that minimize conditional value-at-risk and investigate two performance attributes, asset allocation (AA) and the selection effect (SE), as constraints on asset weights. The test portfolio consists of stocks from the Dow Jones Industrial Average index. Values for the performance attributes are established relative to two benchmarks, equi-weighted and price-weighted portfolios of the same stocks. Performance of the optimized portfolios is judged using comparisons of cumulative price and the risk-measures: maximum drawdown, Sharpe ratio, Sortino–Satchell ratio and Rachev ratio. The results suggest that achieving SE performance thresholds requires larger turnover values than that required for achieving comparable AA thresholds. The results also suggest a positive role in price and risk-measure performance for the imposition of constraints on AA and SE.

scholarly journals A VaR-Type Risk Measure Derived from Cumulative Parisian Ruin for the Classical Risk Model

Risks ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 85 ◽  
Author(s):  
Mohamed Lkabous ◽  
Jean-François Renaud
Keyword(s):  
Risk Model ◽  
Risk Measures ◽  
Risk Measure ◽  
Short Paper ◽  
Classical Risk Model ◽  
Parisian Ruin ◽  
The Classical Risk Model

In this short paper, we study a VaR-type risk measure introduced by Guérin and Renaud and which is based on cumulative Parisian ruin. We derive some properties of this risk measure and we compare it to the risk measures of Trufin et al. and Loisel and Trufin.

CAPITAL ALLOCATION WITH MULTIVARIATE RISK MEASURES: AN AXIOMATIC APPROACH

2019 ◽  
Vol 34 (2) ◽  
pp. 297-315
Author(s):  
Linxiao Wei ◽  
Yijun Hu
Keyword(s):  
Standard Deviation ◽  
Portfolio Management ◽  
Risk Measures ◽  
Risk Measure ◽  
Axiomatic Approach ◽  
Capital Allocation ◽  
Axiom System ◽  
Multivariate Risk ◽  
Multivariate Risk Measures ◽  
Multivariate Risk Measure

AbstractCapital allocation is of central importance in portfolio management and risk-based performance measurement. Capital allocations for univariate risk measures have been extensively studied in the finance literature. In contrast to this situation, few papers dealt with capital allocations for multivariate risk measures. In this paper, we propose an axiom system for capital allocation with multivariate risk measures. We first recall the class of the positively homogeneous and subadditive multivariate risk measures, and provide the corresponding representation results. Then it is shown that for a given positively homogeneous and subadditive multivariate risk measure, there exists a capital allocation principle. Furthermore, the uniqueness of the capital allocation principe is characterized. Finally, examples are also given to derive the explicit capital allocation principles for the multivariate risk measures based on mean and standard deviation, including the multivariate mean-standard-deviation risk measures.

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