Utility Maximization Under Bounded Expected Loss

Gabih, Abdelali; Sass, Jörn; Wunderlich, Ralf

doi:10.1080/15326340903088495

Cited by 29 publications

(27 citation statements)

References 18 publications

(50 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The existence of λ * ≥ 0, such that E[L(−H λ * (ydQ/dP ))] = x 1 was proven in Lemma 3.9. Furthermore, by (14) we have…”

Section: Main Theoremmentioning

confidence: 97%

Portfolio optimization under shortfall risk constraint

Janke¹,

Li²

2016

Optimization

View full text Add to dashboard Cite

This paper solves a utility maximization problem under utility-based shortfall risk constraint, by proposing an approach using Lagrange multiplier and convex duality. Under mild conditions on the asymptotic elasticity of the utility function and the loss function, we find an optimal wealth process for the constrained problem and characterize the bi-dual relation between the respective value functions of the constrained problem and its dual. This approach applies to both complete and incomplete markets. Moreover, the extension to more complicated cases is illustrated by solving the problem with a consumption process added. Finally, we give an example of utility and loss functions in the Black-Scholes market where the solutions have explicit forms.If the price process S is locally bounded, then it is a local martingale under any equivalent local martingale measure Q on [0, T ]. Moreover, we denote by D(Q) the set of all Radon-Nikodym derivatives dQ/dP for any probability measure Q ∈ Q with respect to P .Assumption 2.2 We assume throughout the paper that Q = ∅.

show abstract

“…The existence of λ * ≥ 0, such that E[L(−H λ * (ydQ/dP ))] = x 1 was proven in Lemma 3.9. Furthermore, by (14) we have…”

Section: Main Theoremmentioning

confidence: 97%

Portfolio optimization under shortfall risk constraint

Janke¹,

Li²

2016

Optimization

View full text Add to dashboard Cite

show abstract

“…Such problems are examined in [10], where the shortfall risk is measured in terms of the expected loss and applied in a static manner.…”

Section: The Normal Distribution and The Inverse Distribution Functiomentioning

confidence: 99%

“…This encouraged researchers to consider a risk measure that is based on the risk neutral expectation of loss -the Limited Expected Loss (LEL). The work of [4] is extended by Gabih, Sass and Wunderlich [10] to cover the case of bounded Expected Loss.…”

Section: Introductionmentioning

confidence: 99%

Portfolio optimization under dynamic risk constraints: Continuous vs. discrete time trading

Redeker

Wunderlich

2017

Statistics &Amp; Risk Modeling

Self Cite

View full text Add to dashboard Cite

Abstract:We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk measure. For continuous-and discrete-time financial markets we investigate the loss in expected utility of intermediate consumption and terminal wealth caused by imposing a dynamic risk constraint. We derive the dynamic programming equations for the resulting stochastic optimal control problems and solve them numerically. Our numerical results indicate that the loss of portfolio performance is not too large while the risk is notably reduced. We then investigate time discretization effects and find that the loss of portfolio performance resulting from imposing a risk constraint is typically bigger than the loss resulting from infrequent trading.

show abstract

“…Observe that ρ is not cash-invariant and thus not a risk measure in the sense of Definition 1.1. But their risk constraint can be reformulated in terms of a utility-based shortfall risk measure which can be interpreted as a limiting case of GUNDEL and WEBER [2008], see GABIH, SASS and WUNDERLICH [2007].…”

Section: Static Risk Constraintsmentioning

confidence: 99%