When do jumps matter for portfolio optimization? : [Version 29 April 2013]

  • We consider the continuous-time portfolio optimization problem of an investor with constant relative risk aversion who maximizes expected utility of terminal wealth. The risky asset follows a jump-diffusion model with a diffusion state variable. We propose an approximation method that replaces the jumps by a diffusion and solve the resulting problem analytically. Furthermore, we provide explicit bounds on the true optimal strategy and the relative wealth equivalent loss that do not rely on results from the true model. We apply our method to a calibrated affine model and fine that relative wealth equivalent losses are below 1.16% if the jump size is stochastic and below 1% if the jump size is constant and γ ≥ 5. We perform robustness checks for various levels of risk-aversion, expected jump size, and jump intensity.

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Author:Marius Ascheberg, Nicole BrangerORCiDGND, Holger KraftGND
Parent Title (German):SAFE working paper series ; No. 16
Series (Serial Number):SAFE working paper series (16)
Place of publication:Frankfurt am Main
Document Type:Working Paper
Year of Completion:2013
Year of first Publication:2013
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2013/06/27
Tag:jumps; optimal investment; stochastic volatility; welfare loss
Issue:Version 29 April 2013
Page Number:34
Institutes:Wirtschaftswissenschaften / Wirtschaftswissenschaften
Wissenschaftliche Zentren und koordinierte Programme / House of Finance (HoF)
Wissenschaftliche Zentren und koordinierte Programme / Center for Financial Studies (CFS)
Dewey Decimal Classification:3 Sozialwissenschaften / 33 Wirtschaft / 330 Wirtschaft
Licence (German):License LogoDeutsches Urheberrecht