The Stability of the Constrained Utility Maximization Problem - A BSDE Approach

Mocha, Markus; Westray, Nicholas

doi:10.48550/arxiv.1107.0190

Cited by 1 publication

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“…In what follows we extend their reasoning to the unbounded case under exponential moments which was thoroughly investigated in [24] where the corresponding assumption is Assumption 2.3. For all > 0 we have that…”

Section: It Is Shown Inmentioning

confidence: 98%

“…However, for power utility maximization, the additive formulation and the setting here are equivalent. We refer the reader to [24] for further details.…”

Section: It Is Shown Inmentioning

confidence: 99%

“…We also state here a representation of the dual optimizer shown in [19] when S is one-dimensional and extended in [24] to the current framework. Using the continuity of the filtration, there exists a continuous local martingale N which is orthogonal to M , i.e.…”

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confidence: 99%

“…We then recall from [24] that if Assumption 2.3 holds and if ( X, Ŷ ) is the solution to the primal and dual optimization problem, then Ψ ∈ E. With regards to the derivation of the BSDE satisfied by Ψ, we note that, using the formulae for X and Ŷ ,…”

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confidence: 99%

“…Those existence results were subsequently extended by Morlais [26], Briand and Hu [5,6], Delbaen, Hu and Richou [7] as well as Barrieu and El Karoui [3]. In particular, the assumption that the mean-variance tradeoff process be bounded has been weakened to it having certain exponential moments, see Mocha and Westray [24,25].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

BSDEs in utility maximization with BMO market price of risk

Frei¹,

Mocha²,

Westray³

2012

Stochastic Processes and their Applications

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This article studies quadratic semimartingale BSDEs arising in power utility maximization when the market price of risk is of BMO type. In a Brownian setting we provide a necessary and sufficient condition for the existence of a solution but show that uniqueness fails to hold in the sense that there exists a continuum of distinct square-integrable solutions. This feature occurs since, contrary to the classical Itô representation theorem, a representation of random variables in terms of stochastic exponentials is not unique. We study in detail when the BSDE has a bounded solution and derive a new dynamic exponential moments condition which is shown to be the minimal sufficient condition in a general filtration. The main results are complemented by several interesting examples which illustrate their sharpness as well as important properties of the utility maximization BSDE.

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Section: It Is Shown Inmentioning

confidence: 98%

“…However, for power utility maximization, the additive formulation and the setting here are equivalent. We refer the reader to [24] for further details.…”

Section: It Is Shown Inmentioning

confidence: 99%