Optimizing Conditional Value-at-Risk in Dynamic Pricing

OR Spectrum 40 (2018), pp. 711-750, doi: 10.1007/s00291-018-0513-7

45 Pages Posted: 6 Mar 2018 Last revised: 6 Aug 2018

See all articles by Jochen Gönsch

Jochen Gönsch

University of Duisburg-Essen - Mercator School of Management

Michael Hassler

University of Augsburg

Rouven Schur

University of Augsburg - Department of Analytics & Optimization

Date Written: December 21, 2017

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. We add to the scarce literature on risk aversion by considering the risk measure Conditional Value-at-Risk (CVaR), which recently became popular in areas like finance, energy or supply chain management. A key aspect of this paper is selling a single unit of capacity, which is highly relevant in, for example, the real estate market. We analytically derive the optimal policy and obtain structural results. The most important managerial implication is that the risk-averse optimal price is constant over large parts of the selling horizon, whereas the price continuously declines in the standard setting of risk-neutral dynamic pricing. This offers a completely new explanation for the price-setting behavior often observed in practice. For arbitrary capacity, we develop two algorithms to efficiently compute the value function and evaluate them in a numerical study. Our results show that applying a risk-averse policy, even a static one, often yields a higher CVaR than applying a dynamic, but risk-neutral, policy.

Keywords: Revenue Management, Dynamic Pricing, Dynamic Programming, Risk Management, Service Operations

JEL Classification: L93, L91, M10, M31, C44, C61

Suggested Citation

Gönsch, Jochen and Hassler, Michael and Schur, Rouven, Optimizing Conditional Value-at-Risk in Dynamic Pricing (December 21, 2017). OR Spectrum 40 (2018), pp. 711-750, doi: 10.1007/s00291-018-0513-7, Available at SSRN: https://ssrn.com/abstract=3130054

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

Rouven Schur

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

Universitätsstraße 2
Augsburg, 86135
Germany

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