Next Article in Journal
Information-Based Trade in German Real Estate and Equity Markets
Previous Article in Journal / Special Issue
Production Flexibility and Hedging
Article Menu

Export Article

Open AccessArticle
Risks 2015, 3(4), 553-572; doi:10.3390/risks3040553

Stochastic Optimal Control for Online Seller under Reputational Mechanisms

1
Mathematics of Networks and Systems, Bell Labs, 600 Mountain Avenue, Murray Hill, NJ 07974, USA
2
Department of Mathematics, Kettering University, Flint, MI 48504, USA
3
Department of Statistics and Probability and Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
*
Author to whom correspondence should be addressed.
Academic Editors: Emiliano A. Valdez and Nick Costanzino
Received: 28 August 2015 / Accepted: 25 November 2015 / Published: 4 December 2015
(This article belongs to the Special Issue Recent Advances in Mathematical Modeling of the Financial Markets)
View Full-Text   |   Download PDF [1503 KB, uploaded 9 December 2015]   |  

Abstract

In this work we propose and analyze a model which addresses the pulsing behavior of sellers in an online auction (store). This pulsing behavior is observed when sellers switch between advertising and processing states. We assert that a seller switches her state in order to maximize her profit, and further that this switch can be identified through the seller’s reputation. We show that for each seller there is an optimal reputation, i.e., the reputation at which the seller should switch her state in order to maximize her total profit. We design a stochastic behavioral model for an online seller, which incorporates the dynamics of resource allocation and reputation. The design of the model is optimized by using a stochastic advertising model from [1] and used effectively in the Stochastic Optimal Control of Advertising [2]. This model of reputation is combined with the effect of online reputation on sales price empirically verified in [3]. We derive the Hamilton-Jacobi-Bellman (HJB) differential equation, whose solution relates optimal wealth level to a seller’s reputation. We formulate both a full model, as well as a reduced model with fewer parameters, both of which have the same qualitative description of the optimal seller behavior. Coincidentally, the reduced model has a closed form analytical solution that we construct. View Full-Text
Keywords: Stochastic optimal control models; online stores; Hamilton-Jacobi-Bellman equation Stochastic optimal control models; online stores; Hamilton-Jacobi-Bellman equation
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Bradonjić, M.; Causley, M.; Cohen, A. Stochastic Optimal Control for Online Seller under Reputational Mechanisms. Risks 2015, 3, 553-572.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Risks EISSN 2227-9091 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top