Faculty of Economics and Business Administration Publications Database

When do jumps matter for portfolio optimization?

Ascheberg, Marius
Branger, Nicole
Seifried, Frank Thomas
Volume: 16
Number: 8
Pages: 1297 - 1311
ISSN-Print: 1469-7688
Link External Source: Online Version
Year: 2016
Keywords: Optimal investment; Jumps; Stochastic volatility; Welfare loss

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.