scholarly journals Optimization Problem of Insurance Investment Based on Spectral Risk Measure and RAROC Criterion

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Xia Zhao ◽  
Hongyan Ji ◽  
Yu Shi
Keyword(s):  
Risk Aversion ◽  
Optimization Problem ◽  
Risk Measures ◽  
Risk Measure ◽  
Risk Attitude ◽  
Investment Strategy ◽  
Marginal Effect ◽  
Investment Ratio ◽  
Spectral Risk Measure ◽  
The Impact

This paper introduces spectral risk measure (SRM) into optimization problem of insurance investment. Spectral risk measure could describe the degree of risk aversion, so the underlying strategy might take the investor's risk attitude into account. We establish an optimization model aiming at maximizing risk-adjusted return of capital (RAROC) involved with spectral risk measure. The theoretical result is derived and empirical study is displayed under different risk measures and different confidence levels comparatively. The result shows that risk attitude has a significant impact on investment strategy. With the increase of risk aversion factor, the investment ratio of risk asset correspondingly reduces. When the aversive level increases to a certain extent, the impact on investment strategies disappears because of the marginal effect of risk aversion. In the case of VaR and CVaR without regard for risk aversion, the investment ratio of risk asset is increasing significantly.

scholarly journals The theory and application of spectral risk measures in Vietnam

2017 ◽  
Vol 24 (04) ◽  
pp. 29-45
Author(s):  
Hai Ho Hong ◽  
Hoa Nguyen Thi
Keyword(s):  
Risk Aversion ◽  
Portfolio Management ◽  
Value At Risk ◽  
Utility Theory ◽  
Risk Measures ◽  
Risk Measure ◽  
Coherent Risk ◽  
Spectral Risk Measures ◽  
Spectral Risk Measure ◽  
Current Risk

This paper aims to provide a new risk measure for portfolio management in Vietnam by incorporating investor’s risk aversion into current risk measures such as value at risk (VaR) and expected shortfall (ES). This measure shares several desirable characteristics with the coherent risk measures, as illustrated in Artzner et al. (1997). In Vietnam, our study makes the first attempt to utilize distortion theory, instead of utility theory, to facilitate the adoption of risk aversion level in the popular risk measures. We find that spectral risk measure is more flexible and effective to different groups of risk-adverse investors, compared to the more monotonic and conventional VaR and ES measures

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 Optimal Design of Dynamic Default Risk Measures

2012 ◽  
Vol 49 (4) ◽  
pp. 967-977 ◽  
Author(s):  
Leo Shen ◽  
Robert Elliott
Keyword(s):  
Optimal Design ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Continuous Time ◽  
Default Risk ◽  
Optimization Problem ◽  
Risk Measures ◽  
Risk Measure ◽  
Jump Process ◽  
Entropic Risk Measure

We consider the question of an optimal transaction between two investors to minimize their risks. We define a dynamic entropic risk measure using backward stochastic differential equations related to a continuous-time single jump process. The inf-convolution of dynamic entropic risk measures is a key transformation in solving the optimization problem.

BEHAVIORAL PORTFOLIO CHOICE UNDER HYPERBOLIC ABSOLUTE RISK AVERSION

2020 ◽  
Vol 23 (07) ◽  
pp. 2050045
Author(s):  
MARCOS ESCOBAR-ANEL ◽  
ANDREAS LICHTENSTERN ◽  
RUDI ZAGST
Keyword(s):  
Risk Aversion ◽  
Utility Function ◽  
Prospect Theory ◽  
Portfolio Selection ◽  
Continuous Time ◽  
Absolute Risk ◽  
Investment Strategy ◽  
Absolute Risk Aversion ◽  
Distortion Functions ◽  
The Impact

This paper studies the optimal investment problem for a behavioral investor with probability distortion functions and an S-shaped utility function whose utility on gains satisfies the Inada condition at infinity, albeit not necessarily at zero, in a complete continuous-time financial market model. In particular, a piecewise utility function with hyperbolic absolute risk aversion (HARA) is applied. The considered behavioral framework, cumulative prospect theory (CPT), was originally introduced by [A. Tversky & D. Kahneman (1992) Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty 5 (4), 297–323]. The utility model allows for increasing, constant or decreasing relative risk aversion. The continuous-time portfolio selection problem under the S-shaped HARA utility function in combination with probability distortion functions on gains and losses is solved theoretically for the first time, the optimal terminal wealth and its replicating wealth process and investment strategy are stated. In addition, conditions on the utility and the probability distortion functions for well-posedness and closed-form solutions are provided. A specific probability distortion function family is presented which fulfills all those requirements. This generalizes the work by [H. Jin & X. Y. Zhou (2008) Behavioral portfolio selection in continuous time, Mathematical Finance 18 (3), 385–426]. Finally, a numerical case study is carried out to illustrate the impact of the utility function and the probability distortion functions.

scholarly journals An optimal time incentive/disincentive -based compensation in contracts with multiple agents

2016 ◽  
Vol 16 (4) ◽  
pp. 35-53 ◽  
Author(s):  
S. Mahdi Hosseinian
Keyword(s):  
Risk Aversion ◽  
Completion Time ◽  
Optimization Problem ◽  
Risk Attitude ◽  
Theoretical Development ◽  
Optimal Time ◽  
Risk Averse ◽  
Multiple Agents ◽  
Time Saving ◽  
Project Completion

This paper establishes an optimal time incentive/disincentive-based compensation in a contract between a principal and a team of agents. The establishment is based on solving an optimization problem. In order to validate the paper's theoretical development practitioners were engaged in a designed exercise. The paper demonstrates that, at the optimum: the proportion of time incentive/disincentive compensation among agents with the same risk-attitude should reflect the levels of their contributions; the proportion of time incentive/disincentive among agents with the same level of contribution should be lowered for agents with higher levels of risk aversion; and the proportion of time incentive/disincentive to a team of risk averse agents should reduce, and the fixed component of the team fee should increase, when the agents in the team become more risk-averse or the level of the uncertainty in project completion time increases. The paper’s outcome provides guidance to those involved in contracts design for choosing the best way to reward (penalise) multiple agents, form a team, and allow for any time saving (overrun) through the terms of a contract.    

scholarly journals LIQUIDITY RISK AND INSTABILITIES IN PORTFOLIO OPTIMIZATION

2016 ◽  
Vol 19 (05) ◽  
pp. 1650035 ◽  
Author(s):  
FABIO CACCIOLI ◽  
IMRE KONDOR ◽  
MATTEO MARSILI ◽  
SUSANNE STILL
Keyword(s):  
Portfolio Optimization ◽  
Risk Measures ◽  
Risk Measure ◽  
Estimation Error ◽  
Coherent Risk Measures ◽  
Important Special Case ◽  
Coherent Risk ◽  
Finite Samples ◽  
Impact Function ◽  
The Impact

We show that including a term which accounts for finite liquidity in portfolio optimization naturally mitigates the instabilities that arise in the estimation of coherent risk measures on finite samples. This is because taking into account the impact of trading in the market is mathematically equivalent to introducing a regularization on the risk measure. We show here that the impact function determines which regularizer is to be used. We also show that any regularizer based on the norm [Formula: see text] with [Formula: see text] makes the sensitivity of coherent risk measures to estimation error disappear, while regularizers with [Formula: see text] do not. The [Formula: see text] norm represents a border case: its “soft” implementation does not remove the instability, but rather shifts its locus, whereas its “hard” implementation (including hard limits or a ban on short selling) eliminates it. We demonstrate these effects on the important special case of expected shortfall (ES) which has recently become the global regulatory market risk measure.

THE PROPER USE OF RISK MEASURES IN PORTFOLIO THEORY

2005 ◽  
Vol 08 (08) ◽  
pp. 1107-1133 ◽  
Author(s):  
SERGIO ORTOBELLI ◽  
SVETLOZAR T. RACHEV ◽  
STOYAN STOYANOV ◽  
FRANK J. FABOZZI ◽  
ALMIRA BIGLOVA
Keyword(s):  
Portfolio Choice ◽  
Risk Measures ◽  
Risk Measure ◽  
Parametric Models ◽  
Empirical Comparison ◽  
Safety Risk ◽  
Portfolio Choices ◽  
Dispersion Measures ◽  
The Mean ◽  
The Impact

This paper discusses and analyzes risk measure properties in order to understand how a risk measure has to be used to optimize the investor's portfolio choices. In particular, we distinguish between two admissible classes of risk measures proposed in the portfolio literature: safety-risk measures and dispersion measures. We study and describe how the risk could depend on other distributional parameters. Then, we examine and discuss the differences between statistical parametric models and linear fund separation ones. Finally, we propose an empirical comparison among three different portfolio choice models which depend on the mean, on a risk measure, and on a skewness parameter. Thus, we assess and value the impact on the investor's preferences of three different risk measures even considering some derivative assets among the possible choices.

Optimal Design of Dynamic Default Risk Measures

2012 ◽  
Vol 49 (04) ◽  
pp. 967-977
Author(s):  
Leo Shen ◽  
Robert Elliott
Keyword(s):  
Optimal Design ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Continuous Time ◽  
Default Risk ◽  
Optimization Problem ◽  
Risk Measures ◽  
Risk Measure ◽  
Jump Process ◽  
Entropic Risk Measure

We consider the question of an optimal transaction between two investors to minimize their risks. We define a dynamic entropic risk measure using backward stochastic differential equations related to a continuous-time single jump process. The inf-convolution of dynamic entropic risk measures is a key transformation in solving the optimization problem.

Optimal Independent Pricing Strategies of Dual-Channel Supply Chain Based on Risk-Aversion Attitudes

2018 ◽  
Vol 35 (02) ◽  
pp. 1840004 ◽  
Author(s):  
Zheng Liu ◽  
Qi Xu ◽  
Kun Yang
Keyword(s):  
Supply Chain ◽  
Risk Aversion ◽  
Risk Attitude ◽  
Substitution Effect ◽  
Pricing Strategies ◽  
Supply Chain System ◽  
Dual Channel ◽  
Dual Channel Supply Chain ◽  
The Impact ◽  
Independent Model

Dual-channel supply chain system, channel optimization is influenced by channel attitude toward risk, in which risk is classified as general risk and interruption risk. To consider lead time may bring out supply conflicts, substitution effect of online channel and ratio of promotional cost are introduced and an independent model is developed. Based on that, the impact of interruption risk under risk-aversion attitude on both channels is further studied. Finally, it is proved how the risk attitude influences pricing and profit strategy.

scholarly journals Scenario aggregation method for portfolio expectile optimization

2016 ◽  
Vol 33 (1-2) ◽  
Author(s):  
Edgars Jakobsons
Keyword(s):  
Portfolio Optimization ◽  
Value At Risk ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Risk Measures ◽  
Risk Measure ◽  
Conditional Value At Risk ◽  
Aggregation Method ◽  
Portfolio Optimization Problem ◽  
Scenario Aggregation

AbstractThe statistical functional expectile has recently attracted the attention of researchers in the area of risk management, because it is the only risk measure that is both coherent and elicitable. In this article, we consider the portfolio optimization problem with an expectile objective. Portfolio optimization problems corresponding to other risk measures are often solved by formulating a linear program (LP) that is based on a sample of asset returns. We derive three different LP formulations for the portfolio expectile optimization problem, which can be considered as counterparts to the LP formulations for the Conditional Value-at-Risk (CVaR) objective in the works of Rockafellar and Uryasev [

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