OPTIMAL REINSURANCE FROM THE VIEWPOINTS OF BOTH AN INSURER AND A REINSURER UNDER THE CVAR RISK MEASURE AND VAJDA CONDITION

2021 ◽  
pp. 1-29
Author(s):  
Yanhong Chen
Keyword(s):  
Loss Function ◽  
Value At Risk ◽  
Numerical Study ◽  
Risk Measure ◽  
Convex Combination ◽  
Weighting Factor ◽  
Loss Functions ◽  
Conditional Value At Risk ◽  
Optimal Reinsurance ◽  
The Impact

ABSTRACT In this paper, we study the optimal reinsurance contracts that minimize the convex combination of the Conditional Value-at-Risk (CVaR) of the insurer’s loss and the reinsurer’s loss over the class of ceded loss functions such that the retained loss function is increasing and the ceded loss function satisfies Vajda condition. Among a general class of reinsurance premium principles that satisfy the properties of risk loading and convex order preserving, the optimal solutions are obtained. Our results show that the optimal ceded loss functions are in the form of five interconnected segments for general reinsurance premium principles, and they can be further simplified to four interconnected segments if more properties are added to reinsurance premium principles. Finally, we derive optimal parameters for the expected value premium principle and give a numerical study to analyze the impact of the weighting factor on the optimal reinsurance.

scholarly journals Optimal Coordinated Bidding of a Profit Maximizing, Risk-Averse EV Aggregator in Three-Settlement Markets Under Uncertainty

Energies ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1755 ◽  
Author(s):  
Yelena Vardanyan ◽  
Henrik Madsen
Keyword(s):  
Real Time ◽  
Value At Risk ◽  
Risk Measure ◽  
Convex Combination ◽  
Computation Time ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Two Stage ◽  
Mixed Integer Linear Program ◽  
Market Prices

This paper develops a two-stage stochastic and dynamically updated multi-period mixed integer linear program (SD-MILP) for optimal coordinated bidding of an electric vehicle (EV) aggregator to maximize its profit from participating in competitive day-ahead, intra-day and real-time markets. The hourly conditional value at risk (T-CVaR) is applied to model the risk of trading in different markets. The objective of two-stage SD-MILP is modeled as a convex combination of the expected profit and the T-CVaR hourly risk measure. When day-ahead, intra-day and real-time market prices and fleet mobility are uncertain, the proposed two-stage SD-MILP model yields optimal EV charging/discharging plans for day-ahead, intra-day and real-time markets at per device level. The degradation costs of EV batteries are precisely modeled. To reflect the continuous clearing nature of the intra-day and real-time markets, rolling planning is applied, which allows re-forecasting and re-dispatching. The proposed two-stage SD-MILP is used to derive a bidding curve of an aggregator managing 1000 EVs. Furthermore, the model statistics and computation time are recorded while simulating the developed algorithm with 5000 EVs.

scholarly journals EVALUATING THE ACCURACY OF TAIL RISK FORECASTS FOR SYSTEMIC RISK MEASUREMENT

2018 ◽  
Vol 13 (02) ◽  
pp. 1850009 ◽  
Author(s):  
CHRISTIAN BROWNLEES ◽  
GIUSEPPE CAVALIERE ◽  
ALICE MONTI
Keyword(s):  
Mean Square Error ◽  
Financial Institutions ◽  
Loss Function ◽  
Systemic Risk ◽  
Value At Risk ◽  
Risk Measurement ◽  
Loss Functions ◽  
Conditional Value At Risk ◽  
Mean Square ◽  
Tail Risk

In this paper, we address how to evaluate tail risk forecasts for systemic risk (SRISK) measurement. We propose two loss functions, the Tail Tick Loss and the Tail Mean Square Error, to evaluate, respectively, Conditional Value-at-Risk (CoVaR) and MES forecasts. We then analyse CoVaR and MES forecasts for a panel of top US financial institutions between 2000 and 2012 constructed using a set of bivariate DCC-GARCH-type models. The empirical results highlight the importance of using an appropriate loss function for the evaluation of such forecasts. Among other findings, the analysis confirms that the DCC-GJR specification provides accurate predictions for both CoVaR and MES, in particular for the riskiest group of institutions in the panel (Broker-Dealers).

scholarly journals An Asset Allocation Model and Its Solving Method

2017 ◽  
Vol 5 (2) ◽  
pp. 163-175
Author(s):  
Qingye Zhang ◽  
Yan Gao
Keyword(s):  
Asset Allocation ◽  
Value At Risk ◽  
Risk Measure ◽  
Convex Combination ◽  
Conditional Value At Risk ◽  
Smoothing Function ◽  
Smooth Approximation ◽  
Allocation Model ◽  
Risk And Return ◽  
Gradient Algorithms

Abstract Asset allocation is an important issue in finance, and both risk and return are its fundamental ingredients. Rather than the return, the measure of the risk is complicated and of controversy. In this paper, we propose an appropriate risk measure which is precisely a convex combination of mean semi-deviation and conditional value-at-risk. Based on this risk measure, investors can trade-off flexibly between the volatility and the loss to tackle the incurring risk by choosing different convex coefficients. As the presented risk measure contains nonsmooth term, the asset allocation model based on it is nonsmooth. To employ traditional gradient algorithms, we develop a uniform smooth approximation of the plus function and convert the model into a smooth one. Finally, an illustrative empirical study is given. The results indicate that investors can control risk efficiently by adjusting the convex coefficient and the confidence level simultaneously according to their perceptions. Moreover, the effectiveness of the smoothing function proposed in the paper is verified.

scholarly journals Assessing the Impact of the Loss Function, Architecture and Image Type for Deep Learning-Based Wildfire Segmentation

2021 ◽  
Vol 11 (15) ◽  
pp. 7046
Author(s):  
Jorge Francisco Ciprián-Sánchez ◽  
Gilberto Ochoa-Ruiz ◽  
Lucile Rossi ◽  
Frédéric Morandini
Keyword(s):  
Deep Learning ◽  
Loss Function ◽  
State Of The Art ◽  
Fire Detection ◽  
Loss Functions ◽  
Wildfire Spread ◽  
Combine Information ◽  
The Impact ◽  
Image Type ◽  
Segmentation Models

Wildfires stand as one of the most relevant natural disasters worldwide, particularly more so due to the effect of climate change and its impact on various societal and environmental levels. In this regard, a significant amount of research has been done in order to address this issue, deploying a wide variety of technologies and following a multi-disciplinary approach. Notably, computer vision has played a fundamental role in this regard. It can be used to extract and combine information from several imaging modalities in regard to fire detection, characterization and wildfire spread forecasting. In recent years, there has been work pertaining to Deep Learning (DL)-based fire segmentation, showing very promising results. However, it is currently unclear whether the architecture of a model, its loss function, or the image type employed (visible, infrared, or fused) has the most impact on the fire segmentation results. In the present work, we evaluate different combinations of state-of-the-art (SOTA) DL architectures, loss functions, and types of images to identify the parameters most relevant to improve the segmentation results. We benchmark them to identify the top-performing ones and compare them to traditional fire segmentation techniques. Finally, we evaluate if the addition of attention modules on the best performing architecture can further improve the segmentation results. To the best of our knowledge, this is the first work that evaluates the impact of the architecture, loss function, and image type in the performance of DL-based wildfire segmentation models.

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 Risk-Averse Multi-Stage Stochastic Programming to Optimizing Vaccine Allocation and Treatment Logistics for Effective Epidemic Response

2021 ◽  
Author(s):  
Xuecheng Yin ◽  
Esra Buyuktahtakin
Keyword(s):  
Value At Risk ◽  
Virus Disease ◽  
Risk Measure ◽  
Adverse Outcomes ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Expected Number ◽  
Multi Stage ◽  
Stochastic Mixed Integer Programming

Existing compartmental-logistics models in epidemics control are limited in terms of optimizing the allocation of vaccines and treatment resources under a risk-averse objective. In this paper, we present a data-driven, mean-risk, multi-stage, stochastic epidemics-vaccination-logistics model that evaluates various disease growth scenarios under the Conditional Value-at-Risk (CVaR) risk measure to optimize the distribution of treatment centers, resources, and vaccines, while minimizing the total expected number of infections, deaths, and close contacts of infected people under a limited budget. We integrate a new ring vaccination compartment into a Susceptible-Infected-Treated-Recovered-Funeral-Burial epidemics-logistics model. Our formulation involves uncertainty both in the vaccine supply and the disease transmission rate. Here, we also consider the risk of experiencing scenarios that lead to adverse outcomes in terms of the number of infected and dead people due to the epidemic. Combining the risk-neutral objective with a risk measure allows for a trade-off between the weighted expected impact of the outbreak and the expected risks associated with experiencing extremely disastrous scenarios. We incorporate human mobility into the model and develop a new method to estimate the migration rate between each region when data on migration rates is not available. We apply our multi-stage stochastic mixed-integer programming model to the case of controlling the 2018-2020 Ebola Virus Disease (EVD) in the Democratic Republic of the Congo (DRC) using real data. Our results show that increasing the risk-aversion by emphasizing potentially disastrous outbreak scenarios reduces the expected risk related to adverse scenarios at the price of the increased expected number of infections and deaths over all possible scenarios. We also find that isolating and treating infected individuals are the most efficient ways to slow the transmission of the disease, while vaccination is supplementary to primary interventions on reducing the number of infections. Furthermore, our analysis indicates that vaccine acceptance rates affect the optimal vaccine allocation only at the initial stages of the vaccine rollout under a tight vaccine supply.

Risk Measures for Natural Resource Management: Description, Simulation Testing, and R Code With Fisheries Examples

2012 ◽  
Vol 3 (1) ◽  
pp. 150-157 ◽  
Author(s):  
Suresh Andrew Sethi ◽  
Mike Dalton
Keyword(s):  
Natural Resource ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Policy Decision ◽  
Performance Measure ◽  
Small Sample ◽  
Conditional Value At Risk ◽  
Management Scenarios ◽  
Resource Systems

Abstract Traditional measures that quantify variation in natural resource systems include both upside and downside deviations as contributing to variability, such as standard deviation or the coefficient of variation. Here we introduce three risk measures from investment theory, which quantify variability in natural resource systems by analyzing either upside or downside outcomes and typical or extreme outcomes separately: semideviation, conditional value-at-risk, and probability of ruin. Risk measures can be custom tailored to frame variability as a performance measure in terms directly meaningful to specific management objectives, such as presenting risk as harvest expected in an extreme bad year, or by characterizing risk as the probability of fishery escapement falling below a prescribed threshold. In this paper, we present formulae, empirical examples from commercial fisheries, and R code to calculate three risk measures. In addition, we evaluated risk measure performance with simulated data, and we found that risk measures can provide unbiased estimates at small sample sizes. By decomposing complex variability into quantitative metrics, we envision risk measures to be useful across a range of wildlife management scenarios, including policy decision analyses, comparative analyses across systems, and tracking the state of natural resource systems through time.

ASSET CORRELATIONS IN TURBULENT MARKETS AND THE IMPACT OF DIFFERENT REGIMES ON ASSET MANAGEMENT

2011 ◽  
Vol 28 (01) ◽  
pp. 1-23 ◽  
Author(s):  
GERMAN BERNHART ◽  
STEPHAN HÖCHT ◽  
MICHAEL NEUGEBAUER ◽  
MICHAEL NEUMANN ◽  
RUDI ZAGST
Keyword(s):  
Risk Aversion ◽  
Asset Management ◽  
Value At Risk ◽  
Conditional Value At Risk ◽  
Dependence Structure ◽  
The Us ◽  
The Mean ◽  
Asian Market ◽  
Asset Classes ◽  
The Impact

In this article, the dependence structure of the asset classes stocks, government bonds, and corporate bonds in different market environments and its implications on asset management are investigated for the US, European, and Asian market. Asset returns are modelled by a Markov-switching model which allows for two market regimes with completely different risk-return structures. Using major stock indices from all three regions, calm and turbulent market periods are identified for the time period between 1987 and 2009 and the correlation structures in the respective periods are compared. It turns out that the correlations between as well as within the asset classes under investigation are far from being stable and vary significantly between calm and turbulent market periods as well as in time. It also turns out that the US and European markets are much more integrated than the Asian and US/European ones. Moreover, the Asian market features more and longer turbulence phases. Finally, the impact of these findings is examined in a portfolio optimization context. To accomplish this, a case study using the mean-variance and the mean-conditional-value-at-risk framework as well as two levels of risk aversion is conducted. The results show that an explicit consideration of different market conditions in the modelling framework yields better portfolio performance as well as lower portfolio risk compared to standard approaches. These findings hold true for all investigated optimization frameworks and risk-aversion levels.

Coordinating Supply Chain with Buy-Back Contracts in the Presence of Risk Aversion

2018 ◽  
Vol 35 (02) ◽  
pp. 1840008 ◽  
Author(s):  
Chunlin Luo ◽  
Xin Tian ◽  
Xiaobing Mao ◽  
Qiang Cai
Keyword(s):  
Supply Chain ◽  
Risk Aversion ◽  
Value At Risk ◽  
Performance Measure ◽  
Expected Profit ◽  
Conditional Value At Risk ◽  
Allocation Rule ◽  
Risk Averse ◽  
Buy Back ◽  
The Impact

This paper addresses the operational decisions and coordination of the supply chain in the presence of risk aversion, where the risk averse retailer’s performance is measured by a combination of the expected profit and conditional value-at-risk (CVaR). Such performance measure reflects the desire of the retailer to maximize the expected profit on one hand and to control the downside risk of the profit on the other hand. The impact of risk aversion on the supply chain’s decision and performance is also explored. To overcome the inefficiency due to the double marginalization and the aggravation resulting from risk aversion, we investigate the buy-back contract to coordinate the supply chain. Such contract can largely increase the supply chain’s profit, especially when the retailer is more risk averse. Lastly, we extend such risk measure to the widely-used business model nowadays — platform selling model, and explore the impact of the allocation rule on the manufacturer’s decision.

scholarly journals Risk-Limiting Real-Time Economic Dispatch in a Power System with Flexibility Resources

Energies ◽  
2019 ◽  
Vol 12 (16) ◽  
pp. 3133 ◽  
Author(s):  
Hongji Lin ◽  
Chongyu Wang ◽  
Fushuan Wen ◽  
Chung-Li Tseng ◽  
Jiahua Hu ◽  
...  
Keyword(s):  
Power System ◽  
Real Time ◽  
Value At Risk ◽  
Renewable Energy Sources ◽  
Economic Dispatch ◽  
Conditional Value At Risk ◽  
Operational Flexibility ◽  
Practical Applications ◽  
Start Up ◽  
The Impact

The integration of numerous intermittent renewable energy sources (IRESs) poses challenges to the power supply-demand balance due to the inherent intermittent and uncertain power outputs of IRESs, which requires higher operational flexibility of the power system. The deployment of flexible ramping products (FRPs) provides a new alternative to accommodate the high penetration of IRESs. Given this background, a bi-level risk-limiting real-time unit commitment/real-time economic dispatch model considering FRPs provided by different flexibility resources is proposed. In the proposed model, the objective is to maximize the social surplus while minimizing the operational risk, quantified using the concept of conditional value-at-risk (CVaR). Energy and ramping capabilities of conventional generating units during the start-up or shut-down processes are considered, while meeting the constraints including unit start-up/shut-down trajectories and ramping up/down rates in consecutive time periods. The Karush–Kuhn–Tucker (KKT) optimality conditions are then used to convert the bi-level programming problem into a single-level one, which can be directly solved after linearization. The modified IEEE 14-bus power system is employed to demonstrate the proposed method, and the role of FRPs in enhancing the system flexibility and improving the accommodation capability for IRESs is illustrated in some operation scenarios of the sample system. The impact of the confidence level in CVaR on the system operational flexibility is also investigated through case studies. Finally, a case study is conducted on a regional power system in Guangdong Province, China to demonstrate the potential of the proposed method for practical applications.

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