TY - JOUR
T1 - Dynamic Pricing with Surging Demand
AU - Bo , Lijun
AU - Huang , Yijie
JO - CSIAM Transactions on Applied Mathematics
VL - 1
SP - 142
EP - 181
PY - 2024
DA - 2024/02
SN - 5
DO - http://doi.org/10.4208/csiam-am.SO-2023-0034
UR - https://global-sci.org/intro/article_detail/csiam-am/22923.html
KW - Dynamic pricing, surging demand, HJB equation, viscosity solution, linear demand.
AB - <p style="text-align: justify;">This paper considers the case of a firm’s dynamic pricing problem for a nonperishable product experiencing surging demand caused by rare events modelled by
a marked point process. The firm aims to maximize its running revenue by selecting
an optimal price process for the product until its inventory is depleted. Using the dynamic program and inspired by the viscosity solution technique, we solve the resulting
integro-differential Hamilton-Jacobi-Bellman (HJB) equation and prove that the value
function is its unique classical solution. We also establish structural properties for our
problem and find that the optimal price always decreases with initial inventory level
in the absence of surging demand. However, with surging demand, we find that the
optimal price could increase rather than decrease at the initial inventory level.</p>