Time-Consistent, Risk-Averse Dynamic Pricing

European Journal of Operational Research, 277 (2019), pp. 587-603. doi:10.1016/j.ejor.2019.02.0

45 Pages Posted: 11 Mar 2019 Last revised: 12 Jul 2019

See all articles by Rouven Schur

Rouven Schur

University of Augsburg - Department of Analytics & Optimization

Jochen Gönsch

University of Duisburg-Essen - Mercator School of Management

Michael Hassler

University of Augsburg

Date Written: July 1, 2019

Abstract

Many industries use dynamic pricing on an operational level to maximize revenue from selling a fixed capacity over a finite horizon. Classical risk-neutral approaches do not accommodate the risk aversion often encountered in practice. When risk aversion is considered, time-consistency becomes an important issue. In this paper, we use a dynamic coherent risk-measure to ensure that decisions are actually implemented and only depend on states that may realize in the future. In particular, we use the risk measure Conditional Value-at-Risk (CVaR), which recently became popular in areas like finance, energy or supply chain management.

A result is that the risk-averse dynamic pricing problem can be transformed to a classical, risk-neutral problem. To do so, a surprisingly simple modification of the selling probabilities suffices. Thus, all structural properties carry over. Moreover, we show that the risk-averse and the risk-neutral solution of the original problem are proportional under certain conditions, that is, their optimal decision variable and objective values are proportional, respectively. In a small numerical study, we evaluate the risk vs. revenue trade-off and compare the new approach with existing approaches from literature.

This has straightforward implications for practice. On the one hand, it shows that existing dynamic pricing algorithms and systems can be kept in place and easily incorporate risk aversion. On the other hand, our results help to understand many risk-averse decision makers who often use “conservative” estimates of selling probabilities or discount optimal prices.

Keywords: Revenue Management, Dynamic Pricing, Risk Aversion, Conditional Value-at-Risk

Suggested Citation

Schur, Rouven and Gönsch, Jochen and Hassler, Michael, Time-Consistent, Risk-Averse Dynamic Pricing (July 1, 2019). European Journal of Operational Research, 277 (2019), pp. 587-603. doi:10.1016/j.ejor.2019.02.0, Available at SSRN: https://ssrn.com/abstract=3338338

Rouven Schur

University of Augsburg - Department of Analytics & Optimization ( email )

Universitätsstraße 2
Augsburg, 86135
Germany

Jochen Gönsch (Contact Author)

University of Duisburg-Essen - Mercator School of Management ( email )

Lotharstraße 65
Duisburg, Nordrhein-Westfalen 47057
Germany
+49 203 379 - 2777 (Phone)
+49 203 379 - 1760 (Fax)

HOME PAGE: http://udue.de/goensch

Michael Hassler

University of Augsburg ( email )

Universitätsstr. 2
Augsburg, 86159
Germany

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