Robust Preferences and Robust Portfolio Choice

Schied, Alexander; Föllmer, Hans; Weber, Stefan

doi:10.1016/s1570-8659(08)00002-1

Cited by 36 publications

(11 citation statements)

References 115 publications

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“…Below we focus directly on their static counterparts. For more details we refer, e.g., to Schied et al (2009) or Föllmer and Schied (2016). In addition, to ensure that all our problems are well defined, we assume throughout that X consists of P-bounded random variables.…”

Section: Adjusting Es Via Benchmark Es Profilesmentioning

confidence: 99%

Adjusted Expected Shortfall

Burzoni

Munari

Wang

2020

Preprint

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We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding adjusted Expected Shortfalls quantify risk as the minimum amount of capital that has to be raised and injected into a financial position X to ensure that Expected Shortfall ES p (X) does not exceed a pre-specified threshold g(p) for every probability level p ∈ [0, 1]. Through the choice of the benchmark risk profile g one can tailor the risk assessment to the specific application of interest. We devote special attention to the study of risk profiles defined by the Expected Shortfall of a benchmark random loss, in which case our risk measures are intimately linked to second-order stochastic dominance.

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Section: Adjusting Es Via Benchmark Es Profilesmentioning

confidence: 99%

Adjusted Expected Shortfall

Burzoni

Munari

Wang

2020

Preprint

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“…The robust approach assumes that the modeler surrounds an approximating model by introducing a family of "neighborhood" models via perturbations. Schied et al [24] gave a good survey on the theory of robust preferences and robust portfolio selection. Particularly, Schied et al [24] considered a dynamic version of model uncertainty, where the uncertain drift of the risky asset price process was assumed to be stochastic and time-dependent.…”

Section: Yang Shen and Tak Kuen Siumentioning

confidence: 99%

“…Schied et al [24] gave a good survey on the theory of robust preferences and robust portfolio selection. Particularly, Schied et al [24] considered a dynamic version of model uncertainty, where the uncertain drift of the risky asset price process was assumed to be stochastic and time-dependent. For a systematic account of robustness and model uncertainty in economic modeling, one may also refer to Hansen and Sargent [12].…”

Section: Yang Shen and Tak Kuen Siumentioning

confidence: 99%

Consumption-portfolio optimization and filtering in a hidden Markov-modulated asset price model

Shen

Siu²

2017

Journal of Industrial &Amp; Management Optimization

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We study a consumption-portfolio optimization problem in a hidden Markov-modulated asset price model with multiple risky assets, where model uncertainty is present. Under this modeling framework, the appreciation rates of risky shares are modulated by a continuous-time, finite-state hidden Markov chain whose states represent different modes of the model. We consider the situation where an economic agent only has access to information about the price processes of risky shares and aims to maximize the expected, discounted utility from intermediate consumption and terminal wealth within a finite horizon. The standard innovations approach in filtering theory is then used to transform the partially observed consumption-portfolio optimization problem to the one with complete observations. Robust filters of the chain and estimates of some other parameters are presented. Using the stochastic maximum principle, we derive a closed-form solution of an optimal consumptionportfolio strategy in the case of a power utility.

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“…Here, "≪" denotes the absolute continuity and Q denotes the true transition kernel of the underlying MCP, while γ 1 and γ 2 control the degree of variation between the estimated transition kernel and its true model. In particular, if γ 1 = 0, it becomes the average value at risk (see [40,44] and references therein). It is also notable that each concave and homogeneous valuation function has one dual representation of the form (9) under some regularity conditions for the set P (see e.g.…”

Section: Examplesmentioning

confidence: 99%

Risk-Sensitive Markov Control Processes

Shen¹,

Stannat²,

Obermayer³

2013

SIAM J. Control Optim.

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We introduce the Lyapunov approach to optimal control problems of average risk-sensitive Markov control processes with general risk maps. Motivated by applications in particular to behavioral economics, we consider possibly nonconvex risk maps, modeling behavior with mixed risk preference. We introduce classical objective functions to the risk-sensitive setting and we are in particular interested in optimizing the average risk in the infinite-time horizon for Markov Control Processes on general, possibly non-compact, state spaces allowing also unbounded cost. Existence and uniqueness of an optimal control is obtained with a fixed point theorem applied to the nonlinear map modeling the risksensitive expected total cost. The necessary contraction is obtained in a suitable chosen seminorm under a new set of conditions: 1) Lyapunov-type conditions on both risk maps and cost functions that control the growth of iterations, and 2) Doeblin-type conditions, known for Markov chains, generalized to nonlinear mappings. In the particular case of the entropic risk map, the above conditions can be replaced by the existence of a Lyapunov function, a local Doeblin-type condition for the underlying Markov chain, and a growth condition on the cost functions.

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Robust Preferences and Robust Portfolio Choice

Cited by 36 publications

References 115 publications

Adjusted Expected Shortfall

Adjusted Expected Shortfall

Consumption-portfolio optimization and filtering in a hidden Markov-modulated asset price model

Risk-Sensitive Markov Control Processes

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