Option pricing for an uncertain stock model with jumps

By means of uncertain differential equation, an uncertain stock model usually describes the evolution of the stock price which highly depends on human uncertainty. Considering the sudden drifts on the stock price which might be caused by war, policy or technology, this paper proposes an uncertain stock model with both positive jumps and negative jumps in form of uncertain differential equation with jumps. European option pricing formulas for the proposed stock model are derived, and its monotonicity with respect to the parameters such as initial price, expiration date, and strike price is also studied.