Greed, Leverage, and Potential Losses: A Prospect Theory Perspective

Jin, Hanqing; Zhou, Xun Yu

doi:10.1111/j.1467-9965.2011.00490.x

Cited by 54 publications

(27 citation statements)

References 13 publications

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“…We will prove this equivalence in Theorem 4 and stress its relevance in Section 2.4. Notice that decision-making driven by targets' achievement is not only intuitive but also widely accepted and supported by the economics literature, see for instance the classical works of Kahneman & Tversky (1979) and Tversky & Kahneman (1992) on Prospect Theory and, more recently, Bordley & Li Calzi (2000) and Jin & Zhou (2009).…”

Section: Quadratic Loss Function: the Target-based Approachmentioning

confidence: 99%

On efficiency of mean–variance based portfolio selection in defined contribution pension schemes

Vigna

2012

Quantitative Finance

103

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We consider the portfolio selection problem in the accumulation phase of a defined contribution (DC) pension scheme. We solve the mean-variance portfolio selection problem using the embedding technique pioneered by Zhou & Li (2000) and show that it is equivalent to a targetbased optimization problem, consisting in the minimization of a quadratic loss function. We support the use of the target-based approach in DC pension funds for three reasons. Firstly, it transforms the difficult problem of selecting the individual's risk aversion coefficient into the easier task of choosing an appropriate target. Secondly, it is intuitive, flexible and adaptable to the member's needs and preferences. Thirdly, it produces final portfolios that are efficient in the mean-variance setting.We address the issue of comparison between an efficient portfolio and a portfolio that is optimal according to the more general criterion of maximization of expected utility (EU). The two natural notions of Variance Inefficiency and Mean Inefficiency are introduced, which measure the distance of an optimal inefficient portfolio from an efficient one, focusing on their variance and on their expected value, respectively. We illustrate the general procedure for finding the mean-variance inefficiency for the HARA class of utility functions, and then focus on the popular classes of CARA and CRRA utility functions. In these cases we prove the intuitive but not trivial results that the mean-variance inefficiency decreases with the risk aversion of the individual and increases with the time horizon and the Sharpe ratio of the risky asset. As a byproduct we prove that the CARA and CRRA optimal portfolio are not mean-variance efficient.Numerical investigations stress the impact of the time horizon on the extent of mean-variance inefficiency of CARA and CRRA utility functions. While at instantaneous level EU-optimality and efficiency coincide (see Merton (1971)), we find that for short durations they do not differ significantly. However, for longer durations -that are typical in pension funds -the extent of inefficiency turns out to be remarkable and should be taken into account by pension fund investment managers seeking appropriate rules for portfolio selection. Indeed, we see this result as a fourth reason for supporting the use of the target-based approach in DC pension schemes.

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Section: Quadratic Loss Function: the Target-based Approachmentioning

confidence: 99%

On efficiency of mean–variance based portfolio selection in defined contribution pension schemes

Vigna

2012

Quantitative Finance

103

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“…Now that we have solved the negative part problem (9), and the positive part problem First of all, in view of Theorem 3, we only need to consider the following problem in lieu of (10), where (c, c 2 , x + ) are the decision variables:…”

Section: Solution Of the Behavioral Modelmentioning

confidence: 99%

“…Jin and Zhou (2009) prove that potential losses can be catastrophically large with a sufficiently strong agent greed (as reflected by a very high reference point). In other words, when one loses one can lose real big.…”

Section: Introductionmentioning

confidence: 99%

Behavioral portfolio selection with loss control

Zhang

Jin

Zhou

2011

Acta. Math. Sin.-English Ser.

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In this paper we formulate a continuous-time behavioral (à la cumulative prospect theory) portfolio selection model where the losses are constrained by a pre-specified upper bound. Economically the model is motivated by the previously proved fact that the losses occurring in a bad state of the world can be catastrophic for an unconstrained model. Mathematically solving the model boils down to solving a concave Choquet minimization problem with an additional upper bound. We derive the optimal solution explicitly for such a loss control model. The optimal terminal wealth profile is in general characterized by three pieces: the agent has gains in the good states of the world, gets a moderate, endogenously constant loss in the intermediate states, and suffers the maximal loss (which is the given bound for losses) in the bad states. Examples are given to illustrate the general results.

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“…Similar assumptions have been used in Jin and Zhou [45] in their study of portfolio choice under prospect theory, in He and Zhou [46] in their study of a portfolio choice problem under Yaari's [22] dual theory of choice, in Jin and Zhou [47] in their study of greed and leverage within a portfolio choice problem under prospect theory and in Carlier and Dana [48] in their study of the demand for contingent claims under rank-dependent expected utility [21]. Furthermore, note that when both the insured and the insurer are Bayesian decision makers, that is when the insurer does not distort probabilities, then Assumption 7 and Assumption 5 are equivalent 4 .…”

Section: Assumption 7 the Function T þ ñ T 1 P1´tqmentioning

confidence: 95%

Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer

Amarante

Ghossoub

2015

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract: In the classical expected utility framework, a problem of optimal insurance design with a premium constraint is equivalent to a problem of optimal insurance design with a minimum expected retention constraint. When the insurer has ambiguous beliefs represented by a non-additive probability measure, as in Schmeidler, this equivalence no longer holds. Recently, Amarante, Ghossoub and Phelps examined the problem of optimal insurance design with a premium constraint when the insurer has ambiguous beliefs. In particular, they showed that when the insurer is ambiguity-seeking, with a concave distortion of the insured's probability measure, then the optimal indemnity schedule is a state-contingent deductible schedule, in which the deductible depends on the state of the world only through the insurer's distortion function. In this paper, we examine the problem of optimal insurance design with a minimum expected retention constraint, in the case where the insurer is ambiguity-seeking. We obtain the aforementioned result of Amarante, Ghossoub and Phelps and the classical result of Arrow as special cases. Terms of use: Documents in

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Greed, Leverage, and Potential Losses: A Prospect Theory Perspective

Cited by 54 publications

References 13 publications

On efficiency of mean–variance based portfolio selection in defined contribution pension schemes

On efficiency of mean–variance based portfolio selection in defined contribution pension schemes

Behavioral portfolio selection with loss control

Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer

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