When do jumps matter for portfolio optimization?

  • 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 quantities known only in the true model. We apply our method to a calibrated affine model. Our findings are threefold: Jumps matter more, i.e. our approximation is less accurate, if (i) the expected jump size or (ii) the jump intensity is large. Fixing the average impact of jumps, we find that (iii) rare, but severe jumps matter more than frequent, but small jumps.

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Author:Marius Ascheberg, Nicole BrangerORCiDGND, Holger KraftGND, Frank Thomas Seifried
Parent Title (English):SAFE working paper series ; No. 16 [Version November 25, 2015]
Series (Serial Number):SAFE working paper series (16 [Version 2015])
Place of publication:Frankfurt am Main
Document Type:Working Paper
Year of Completion:2015
Year of first Publication:2015
Publishing Institution:Universit├Ątsbibliothek Johann Christian Senckenberg
Release Date:2016/02/02
Tag:jumps; optimal investment; stochastic volatility; welfare loss
Page Number:39
Institutes:Wirtschaftswissenschaften / Wirtschaftswissenschaften
Wissenschaftliche Zentren und koordinierte Programme / House of Finance (HoF)
Wissenschaftliche Zentren und koordinierte Programme / Center for Financial Studies (CFS)
Wissenschaftliche Zentren und koordinierte Programme / Sustainable Architecture for Finance in Europe (SAFE)
Dewey Decimal Classification:3 Sozialwissenschaften / 33 Wirtschaft / 330 Wirtschaft
Licence (German):License LogoDeutsches Urheberrecht