scholarly journals A Portfolio Choice Problem in the Framework of Expected Utility Operators

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 669 ◽  
Author(s):  
Irina Georgescu ◽  
Louis Aimé Fono
Keyword(s):  
Risk Aversion ◽  
Portfolio Choice ◽  
Expected Utility ◽  
Approximate Calculation ◽  
Optimization Problem ◽  
Fuzzy Numbers ◽  
Optimal Allocation ◽  
General Context ◽  
Abstract Theory ◽  
Choice Problem

Possibilistic risk theory starts from the hypothesis that risk is modeled by fuzzy numbers. In particular, in a possibilistic portfolio choice problem, the return of a risky asset will be a fuzzy number. The expected utility operators have been introduced in a previous paper to build an abstract theory of possibilistic risk aversion. To each expected utility operator, one can associate the notion of possibilistic expected utility. Using this notion, we will formulate in this very general context a possibilistic portfolio choice problem. The main results of the paper are two approximate calculation formulas for the corresponding optimization problem. The first formula approximates the optimal allocation with respect to risk aversion and investor’s prudence, as well as the first three possibilistic moments. Besides these parameters, in the second formula, the temperance index of the utility function and the fourth possibilistic moment appear.

scholarly journals The Effect of Prudence on the Optimal Allocation in Possibilistic and Mixed Models

Mathematics ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 133 ◽  
Author(s):  
Irina Georgescu
Keyword(s):  
Risk Aversion ◽  
Portfolio Choice ◽  
Fuzzy Number ◽  
Mixed Models ◽  
Fuzzy Numbers ◽  
Optimal Allocation ◽  
Random Variables ◽  
Background Risk ◽  
Investment Risk ◽  
Approximate Formulas

In this paper, several portfolio choice models are studied: a purely possibilistic model in which the return of the risky is a fuzzy number, and four models in which the background risk appears in addition to the investment risk. In these four models, risk is a bidimensional vector whose components are random variables or fuzzy numbers. Approximate formulas of the optimal allocation are obtained for all models, expressed in terms of some probabilistic or possibilistic moments, depending on the indicators of the investor preferences (risk aversion, prudence).

AMBIGUITY AND PORTFOLIO INERTIA

2002 ◽  
Vol 05 (08) ◽  
pp. 785-795
Author(s):  
MARCELLO BASILI ◽  
FULVIO FONTINI
Keyword(s):  
Portfolio Choice ◽  
Expected Utility ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Specific Structure ◽  
Choice Problem ◽  
Choquet Expected Utility ◽  
Necessary And Sufficient

In this paper the Portfolio Choice problem is studied under ambiguity, formalized by means of the Choquet Expected Utility. Agents are supposed to be Choquet Expected Utility maximizers and are split into two categories: optimists, who hold a concave capacity, and pessimists, who hold a convex one. Portfolio inertia is defined and analyzed. Necessary and sufficient conditions are established between a specific structure of agents' beliefs, namely belief commonality, and Portfolio Inertia.

scholarly journals How the Investor’s Risk Preferences Influence the Optimal Allocation in a Credibilistic Portfolio Problem

2019 ◽  
Vol 7 (4) ◽  
pp. 317-329
Author(s):  
Irina Georgescu ◽  
Jani Kinnunen
Keyword(s):  
Utility Function ◽  
Portfolio Choice ◽  
Expected Utility ◽  
Optimal Allocation ◽  
Fuzzy Variable ◽  
Risky Asset ◽  
Credibility Theory ◽  
Fuzzy Variables ◽  
Portfolio Problem ◽  
Approximation Calculation

Abstract A classical portfolio theory deals with finding the optimal proportion in which an agent invests a wealth in a risk-free asset and a probabilistic risky asset. Formulating and solving the problem depend on how the risk is represented and how, combined with the utility function defines a notion of expected utility. In this paper the risk is a fuzzy variable and the notion of expected utility is defined in the setting of Liu’s credibility theory. Thus, the portfolio choice problem is formulated as an optimization problem in which the objective function is a credibilistic expected utility. Different approximation calculation formulas for the optimal allocation of the credibilistic risky asset are proved. These formulas contain two types of parameters: Various credibilistic moments associated with fuzzy variables (expected value, variance, skewness and kurtosis) and the risk aversion, prudence and temperance indicators of the utility function.

scholarly journals The Willingness to Pay for Diversification

2021 ◽  
Author(s):  
Ola Mahmoud
Keyword(s):  
Willingness To Pay ◽  
Risk Aversion ◽  
Portfolio Choice ◽  
Loss Aversion ◽  
Fundamental Concept ◽  
Decision Makers ◽  
Risk Averse ◽  
Initial Endowment ◽  
Choice Problem

Diversification is a fundamental concept in economics and finance. This paper argues that decision makers have an intrinsic preference for diversification that is responsive to cost and that this willingness to pay for diversification is driven by risk aversion and loss aversion. In an experiment replicating a portfolio choice problem, the value of diversification is estimated to be at 5% of the initial endowment of approximately $100. Moreover, risk-averse and loss-averse individuals are willing to pay more for diversification. These findings point to the idea that diversification is a fundamental preference and may help explain portfolio choice anomalies such as irrational diversification, the diversification bias, and overdiversification. This paper was accepted by Tomasz Piskorski, finance.

scholarly journals General Pareto Optimal Allocations and Applications to Multi-Period Risks

2008 ◽  
Vol 38 (1) ◽  
pp. 105-136 ◽  
Author(s):  
Pauline Barrieu ◽  
Giacomo Scandolo
Keyword(s):  
Expected Utility ◽  
Pareto Optimality ◽  
General Framework ◽  
Optimization Problem ◽  
Optimal Allocation ◽  
Pareto Optimal ◽  
Real Vector ◽  
Optimal Allocations ◽  
Pareto Optimal Allocations

In this paper, we consider the problem of Pareto optimal allocation in a general framework, involving preference functionals defined on a general real vector space. The optimization problem is equivalent to a modified sup-convolution of the different agents’ preference functionals. The results are then applied to a multi-period setting and some further characterization of Pareto optimality for an allocation is obtained for expected utility for processes.

scholarly journals WHEN GAMBLING IS NOT WINNING: EXPLORING OPTIMALITY OF VIX TRADING UNDER THE EXPECTED UTILITY THEORY

2019 ◽  
Vol 1 (1) ◽  
pp. 1-1 ◽  
Author(s):  
Anmar Al Wakil
Keyword(s):  
Risk Aversion ◽  
Portfolio Choice ◽  
Expected Utility ◽  
Risk Premium ◽  
Asset Management ◽  
Utility Theory ◽  
Expected Utility Theory ◽  
Insurance Premium ◽  
Ex Post ◽  
Vix Futures

Recently, financial innovations have given rise to complex derivatives within the asset management industry. Although traditional assets pay dividends or coupons, vIX futures contracts have been partly misunderstood by unsophisticated investors, as they only provide portfolio insurance against stock market crashes. Therefore, over the calmer period 2009-2014, the most traded vIX futures exchange-traded product lost practically all of its value, ruining unexperienced investors. hence, this paper investigates appropriateness of these complex derivatives with investor's risk aversion. We address portfolio-choice optimality under uncertainty, for overlay allocations composed of equities, bonds, and vIX futures. This paper proposes a non-trivial solution based on the expected utility theory to simulate investor's behavior with risk aversion. Furthermore, it derives an investor's surprise metric defined as a welfare criterion measure, and a modelimplied risk premium defined as the insurance premium investor pays ex post to hedge. Empirical results show investing in vIX futures significantly beats traditionally diversified portfolios, but they turn to be particularly inappropriate for risk-loving investors. From the asset management perspective, this paper has practical implications since it recommends pedagogical efforts to raise investors' awareness of overlay strategies.

scholarly journals Portfolio Selection with Subsistence Consumption Constraints and CARA Utility

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Gyoocheol Shim ◽  
Yong Hyun Shin
Keyword(s):  
Portfolio Choice ◽  
Optimization Problem ◽  
Absolute Risk ◽  
Programming Approach ◽  
Optimal Consumption ◽  
Choice Problem ◽  
Dynamic Programming Approach ◽  
Cara Utility ◽  
Constant Absolute Risk Aversion ◽  
Consumption Constraints

We consider the optimal consumption and portfolio choice problem with constant absolute risk aversion (CARA) utility and a subsistence consumption constraint. A subsistence consumption constraint means there exists a positive constant minimum level for the agent’s optimal consumption. We use the dynamic programming approach to solve the optimization problem and also give the verification theorem. We illustrate the effects of the subsistence consumption constraint on the optimal consumption and portfolio choice rules by the numerical results.

scholarly journals General Pareto Optimal Allocations and Applications to Multi-Period Risks

2008 ◽  
Vol 38 (01) ◽  
pp. 105-136 ◽  
Author(s):  
Pauline Barrieu ◽  
Giacomo Scandolo
Keyword(s):  
Expected Utility ◽  
Pareto Optimality ◽  
General Framework ◽  
Optimization Problem ◽  
Optimal Allocation ◽  
Pareto Optimal ◽  
Real Vector ◽  
Optimal Allocations ◽  
Pareto Optimal Allocations

In this paper, we consider the problem of Pareto optimal allocation in a general framework, involving preference functionals defined on a general real vector space. The optimization problem is equivalent to a modified sup-convolution of the different agents’ preference functionals. The results are then applied to a multi-period setting and some further characterization of Pareto optimality for an allocation is obtained for expected utility for processes.

Relative Risk Aversion and Portfolio Choice

2005 ◽  
Author(s):  
Pablo Muñoz Ceballos ◽  
Esteban Flores Díaz
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Portfolio Choice ◽  
Relative Risk Aversion
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