  The prevalence of e-commerce has made detailed customers' personal
information readily accessible to retailers, and this information has been
widely used in pricing decisions. When involving personalized information, how
to protect the privacy of such information becomes a critical issue in
practice. In this paper, we consider a dynamic pricing problem over $T$ time
periods with an \emph{unknown} demand function of posted price and personalized
information. At each time $t$, the retailer observes an arriving customer's
personal information and offers a price. The customer then makes the purchase
decision, which will be utilized by the retailer to learn the underlying demand
function. There is potentially a serious privacy concern during this process: a
third party agent might infer the personalized information and purchase
decisions from price changes from the pricing system. Using the fundamental
framework of differential privacy from computer science, we develop a
privacy-preserving dynamic pricing policy, which tries to maximize the retailer
revenue while avoiding information leakage of individual customer's information
and purchasing decisions. To this end, we first introduce a notion of
\emph{anticipating} $(\varepsilon, \delta)$-differential privacy that is
tailored to dynamic pricing problem. Our policy achieves both the privacy
guarantee and the performance guarantee in terms of regret. Roughly speaking,
for $d$-dimensional personalized information, our algorithm achieves the
expected regret at the order of $\tilde{O}(\varepsilon^{-1} \sqrt{d^3 T})$,
when the customers' information is adversarially chosen. For stochastic
personalized information, the regret bound can be further improved to
$\tilde{O}(\sqrt{d^2T} + \varepsilon^{-2} d^2)$
