Optimal Reciprocal Reinsurance under VaR or TVaR Constraint

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hung-Hsi Huang ◽  
Ching-Ping Wang
Keyword(s):  
At Risk ◽  
Risk Management ◽  
Moral Hazard ◽  
Value At Risk ◽  
Incentive Compatibility ◽  
Regular Form ◽  
Optimal Reinsurance ◽  
The Common ◽  
Risk Constraint ◽  
Management Requirement

Abstract Most existing researches on optimal reinsurance contract are based on an insurer’s viewpoint. However, the optimal reinsurance contract for an insurer is not necessarily to be optimal for a reinsurer. Hence, this study aims to develop the optimal reciprocal reinsurance which satisfies the benefits of both the insurer and reinsurer. Additionally, due to legislative restriction or risk management requirement, the wealth of insurer and reinsurer are frequently imposed upon a VaR (Value-at-Risk) or TVaR (Tail Value-at-Risk) constraint. Therefore, this study develops an optimal reciprocal reinsurance contract which maximizes the common benefits (evaluated by weighted addition of expected utilities) of the insurer and reinsurer subject to their VaR or TVaR constraints. Furthermore, for avoiding moral hazard problem, the developed contract is additionally restricted to a regular form or incentive compatibility (both indemnity schedule and retained loss schedule are continuously nondecreasing).

OPTIMAL REINSURANCE DESIGN WITH DISTORTION RISK MEASURES AND ASYMMETRIC INFORMATION

2021 ◽  
pp. 1-23
Author(s):  
Tim J. Boonen ◽  
Yiying Zhang
Keyword(s):  
At Risk ◽  
Asymmetric Information ◽  
Value At Risk ◽  
Functional Form ◽  
Risk Measures ◽  
Risk Measure ◽  
Incentive Compatibility ◽  
Optimal Reinsurance ◽  
Net Profit ◽  
Distortion Risk Measures

ABSTRACT This paper studies a problem of optimal reinsurance design under asymmetric information. The insurer adopts distortion risk measures to quantify his/her risk position, and the reinsurer does not know the functional form of this distortion risk measure. The risk-neutral reinsurer maximizes his/her net profit subject to individual rationality and incentive compatibility constraints. The optimal reinsurance menu is succinctly derived under the assumption that one type of insurer has a larger willingness to pay than the other type of insurer for every risk. Some comparative analyses are given as illustrations when the insurer adopts the value at risk or the tail value at risk as preferences.

Volatility Forecast by Volatility Index and Its Use as a Risk Management Tool Under a Value-at-Risk Approach

2018 ◽  
Vol 21 (02) ◽  
pp. 1850010 ◽  
Author(s):  
Yam Wing Siu
Keyword(s):  
At Risk ◽  
Risk Management ◽  
Risk Premium ◽  
Value At Risk ◽  
Realized Volatility ◽  
Management Tool ◽  
Spot Price ◽  
Pricing Options ◽  
Significance Levels ◽  
Risk Approach

This paper examines the predicting power of the volatility indexes of VIX and VHSI on the future volatilities (or called realized volatility, [Formula: see text] of their respective underlying indexes of S&P500 Index, SPX and Hang Seng Index, HSI. It is found that volatilities indexes of VIX and VHSI, on average, are numerically greater than the realized volatilities of SPX and HSI, respectively. Further analysis indicates that realized volatility, if used for pricing options, would, on some occasions, result in greatest losses of 2.21% and 1.91% of the spot price of SPX and HSI, respectively while the greatest profits are 2.56% and 2.93% of the spot price of SPX and HSI, respectively, making it not an ideal benchmark for validating volatility forecasting techniques in relation to option pricing. Hence, a new benchmark (fair volatility, [Formula: see text] that considers the premium of option and the cost of dynamic hedging the position is proposed accordingly. It reveals that, on average, options priced by volatility indexes contain a risk premium demanded by the option sellers. However, the options could, on some occasions, result in greatest losses of 4.85% and 3.60% of the spot price of SPX and HSI, respectively while the greatest profits are 4.60% and 5.49% of the spot price of SPX and HSI, respectively. Nevertheless, it can still be a valuable tool for risk management. [Formula: see text]-values of various significance levels for value-at-risk and conditional value-at-value have been statistically determined for US, Hong Kong, Australia, India, Japan and Korea markets.

scholarly journals Optimal reinsurance: a reinsurer’s perspective

2017 ◽  
Vol 12 (1) ◽  
pp. 147-184 ◽  
Author(s):  
Fei Huang ◽  
Honglin Yu
Keyword(s):  
At Risk ◽  
Closed Form ◽  
Value At Risk ◽  
Optimality Criteria ◽  
Total Loss ◽  
Optimal Reinsurance ◽  
Numerical Examples ◽  
Dependency Structure ◽  
Closed Form Solutions

AbstractIn this paper, the optimal safety loading that the reinsurer should set in the reinsurance pricing is studied, which is novel in the literature. It is first assumed that the insurer will choose the form of the reinsurance contract by following the results derived in Cai et al. Different optimality criteria from the reinsurer’s perspective are then studied, such as maximising the expectation of the profit, maximising the utility of the profit and minimising the value-at-risk of the reinsurer’s total loss. By applying the concept of comonotonicity, the problem in which the reinsurer is facing two risks with unknown dependency structure is also solved. Closed-form solutions are obtained when the underlying losses are zero-modified exponentially distributed. Finally, numerical examples are provided to illustrate the results derived.

scholarly journals Using HMM Approach for Assessing Quality of Value at Risk Estimation: Evidence from PSE Listed Company

2017 ◽  
Vol 65 (5) ◽  
pp. 1687-1694
Author(s):  
Tomáš Konderla ◽  
Václav Klepáč
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Stock Exchange ◽  
Risk Estimation ◽  
Listed Company ◽  
Mixture Distribution ◽  
Normal Mixture ◽  
Development Characteristic ◽  
The Common

The article points out the possibilities of using Hidden Markov model (abbrev. HMM) for estimation of Value at Risk metrics (abbrev. VaR) in sample. For the illustration we use data of the company listed on Prague Stock Exchange in range from January 2011 to June 2016. HMM approach allows us to classify time series into different states based on their development characteristic. Due to a deeper shortage of existing domestic results or comparison studies with advanced volatility governed VaR forecasts we tested HMM with univariate ARMA‑GARCH model based VaR estimates. The common testing via Kupiec and Christoffersen procedures offer generalization that HMM model performs better that volatility based VaR estimation technique in terms of accuracy, even with the simpler HMM with normal‑mixture distribution against previously used GARCH with many types of non‑normal innovations.

scholarly journals Risk management of risk under the Basel Accord: forecasting value‐at‐risk of VIX futures

2011 ◽  
Vol 37 (11) ◽  
pp. 1088-1106 ◽  
Author(s):  
Chia‐lin Chang ◽  
Juan‐Ángel Jiménez‐Martín ◽  
Michael McAleer ◽  
Teodosio Pérez‐Amaral
Keyword(s):  
At Risk ◽  
Risk Management ◽  
Value At Risk ◽  
Basel Accord ◽  
Vix Futures ◽  
Management Of Risk

The Value-at-Risk Methodology of Basel II and Basel III

2014 ◽  
pp. 100-114 ◽  
Keyword(s):  
At Risk ◽  
Risk Management ◽  
Value At Risk ◽  
Basel Ii ◽  
Risk Measurement ◽  
Capital Adequacy ◽  
Basel Iii ◽  
Regulatory Capital ◽  
Advantages And Disadvantages ◽  
Risk Methodology

This chapter examines the advantages and disadvantages of the risk estimate approach—Value-at-Risk (VaR) which has been extensively embraced by regulators and practitioners in financial markets under the Basel II & III framework as the basis of risk measurement, both for the purpose of ensuring regulatory capital adequacy, and risk management and strategic planning at industry level.

Arbor City Community Foundation (A): The Foundation

2017 ◽  
pp. 1-3 ◽  
Author(s):  
Karl Schmedders ◽  
Russell Walker ◽  
Michael Stritch
Keyword(s):  
At Risk ◽  
Risk Management ◽  
Value At Risk ◽  
Management Policy ◽  
City Region ◽  
Portfolio Rebalancing ◽  
City Community ◽  
Portfolio Returns ◽  
The Impact ◽  
Community Foundation

The Arbor City Community Foundation (ACCF) was a medium-sized endowment established in Illinois in the late 1970s through the hard work of several local families. The vision of the ACCF was to be a comprehensive center for philanthropy in the greater Arbor City region. ACCF had a fund balance (known collectively as “the fund”) of just under $240 million. The ACCF board of trustees had appointed a committee to oversee investment decisions relating to the foundation assets. The investment committee, under the guidance of the board, pursued an active risk-management policy for the fund. The committee members were primarily concerned with the volatility and distribution of portfolio returns. They relied on the value-at-risk (VaR) methodology as a measurement of the risk of both short- and mid-term investment losses. The questions in Part (A) of the case direct the students to analyze the risk inherent in both one particular asset and the entire ACCF portfolio. For this analysis the students need to calculate daily VaR and monthly VaR values and interpret these figures in the context of ACCF's risk management. In Part (B) the foundation receives a major donation. As a result, the risk inherent in its portfolio changes considerably. The students are asked to evaluate the risk of the fund's new portfolio and to perform a portfolio rebalancing analysis.Understanding the concept of value at risk (VaR); Calculating daily and monthly VaR by two different methods, the historical and the parametric approach; Interpreting the results of VaR calculations; Understanding the role of diversification for managing risk; Evaluating the impact of portfolio rebalancing on the overall risk of a portfolio.

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