Utility maximization with a given pricing measure when the utility is not necessarily concave

Reichlin, Christian

doi:10.1007/s11579-013-0093-x

Cited by 63 publications

(76 citation statements)

References 45 publications

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“…Some properties of

U_{c}

as well as of

{U < U_{c}} : = {(| x \in {double-struckR}_{+}) U (x) < U_{c} (x)}

can be found in Lemma 2.11 of Reichlin (). A key tool to study the relation between U and

U_{c}

is the conjugate of U defined by

J (y) : = \underset{x > 0}{trueprefixsup} {U (x) - x y} .

Because of the nonconcavity of U , the concave envelope

U_{c}

is not necessarily strictly concave and the latter implies that J is no longer smooth; we therefore work with the subdifferential that is denoted by

\partial J

for the convex function J and by

\partial U_{c}

for the concave function

U_{c}

.…”

Section: Problem Formulation and Main Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Behavioral Portfolio Selection: Asymptotics and Stability Along a Sequence of Models

Reichlin

2013

Mathematical Finance

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We consider a sequence of financial markets that converges weakly in a suitable sense and maximize a behavioral preference functional in each market. For expected concave utilities, it is well known that the maximal expected utilities and the corresponding final positions converge to the corresponding quantities in the limit model. We prove similar results for nonconcave utilities and distorted expectations as employed in behavioral finance, and we illustrate by a counterexample that these results require a stronger notion of convergence of the underlying models compared to the concave utility maximization. We use the results to analyze the stability of behavioral portfolio selection problems and to provide numerically tractable methods to solve such problems in complete continuous‐time models.

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“…Some properties of

U_{c}

as well as of

{U < U_{c}} : = {(| x \in {double-struckR}_{+}) U (x) < U_{c} (x)}

can be found in Lemma 2.11 of Reichlin (). A key tool to study the relation between U and

U_{c}

is the conjugate of U defined by

J (y) : = \underset{x > 0}{trueprefixsup} {U (x) - x y} .

Because of the nonconcavity of U , the concave envelope

U_{c}

is not necessarily strictly concave and the latter implies that J is no longer smooth; we therefore work with the subdifferential that is denoted by

\partial J

for the convex function J and by

\partial U_{c}

for the concave function

U_{c}

.…”

Section: Problem Formulation and Main Resultsmentioning

confidence: 99%

“…Our proofs (mainly in the Appendix) use the classical duality relations between

U_{c}

, J ,

\partial J

, and

\partial U_{c}

. Precise statements and proofs can be found in Lemma 2.12 of Reichlin ().…”

Section: Problem Formulation and Main Resultsmentioning

confidence: 99%

Behavioral Portfolio Selection: Asymptotics and Stability Along a Sequence of Models

Reichlin

2013

Mathematical Finance

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“…Reichlin (2013) shows that under some technical assumptions, the maximizer for U C (·) is also the maximizer for U(·). However, this maximizer is only unique under certain cases (see Lemma 5.9 of Reichlin, 2013).…”

Section: Remarkmentioning

confidence: 99%

Rationalizing investors’ choices

Bernard

Chen

Vanduffel

2015

Journal of Mathematical Economics

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“…Certain recursive utility specifications figure in [2,16] but they are very different in spirit from all the other works cited. Due to the mathematical difficulties, continuous-time studies focused mainly on the case of complete markets where every contingent claim can be replicated; see [9,3,22,7,13,36,32,33].…”

Section: Introductionmentioning

confidence: 99%

Existence of solutions in non-convex dynamic programming and optimal investment

2016

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We establish the existence of minimizers in a rather general setting of dynamic stochastic optimization in finite discrete time without assuming either convexity or coercivity of the objective function. We apply this to prove the existence of optimal investment strategies for non-concave utility maximization problems in financial market models with frictions, a first result of its kind. The proofs are based on the dynamic programming principle whose validity is established under quite general assumptions.

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Utility maximization with a given pricing measure when the utility is not necessarily concave

Cited by 63 publications

References 45 publications

Behavioral Portfolio Selection: Asymptotics and Stability Along a Sequence of Models

Behavioral Portfolio Selection: Asymptotics and Stability Along a Sequence of Models

Rationalizing investors’ choices

Existence of solutions in non-convex dynamic programming and optimal investment

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