Wanyang Dai

Wanyang Dai

We formulate a new class of stochastic partial differential equations (SPDEs), named high-order vector backward SPDEs (B-SPDEs) with jumps, which allow the high-order integral-partial differential operators into both drift and diffusion coefficients. Under certain type of Lipschitz and linear growth conditions, we develop a method to prove the existence and uniqueness of adapted solution to these B-SPDEs with jumps. Comparing with the existing discussions on conventional backward stochastic (ordinary) differential equations (BSDEs), we need to handle the differentiability of adapted triplet solution to the B-SPDEs with jumps, which is a subtle part in justifying our main results due to the inconsistency of differential orders on two sides of the B-SPDEs and the partial differential operator appeared in the diffusion coefficient. In addition, we also address the issue about the B-SPDEs under certain Markovian random environment and employ a B-SPDE with strongly nonlinear partial differential operator in the drift coefficient to illustrate the usage of our main results in finance.

Wanyang Dai

Internet of quantum blockchains (IoB) will be the future Internet. In this paper, we make two new contributions to IoB: developing a block based quantum channel networking technology to handle its security modeling in face of the quantum supremacy and establishing IoB based FinTech platform model with dynamic pricing for stable digital currency. The interaction between our new contributions is also addressed. In doing so, we establish a generalized IoB security model by quantum channel networking in terms of both time and space quantum entanglements with quantum key distribution (QKD). Our IoB can interact with general structured things (e.g., supply chain systems) having online trading and payment capability via stable digital currency and can handle vector-valued data streams requiring synchronized services. Thus, within our designed QKD, a generalized random number generator for private and public keys is proposed by a mixed zero-sum and non-zero-sum resource-competition pricing policy. The effectiveness of this policy is justified by diffusion modeling with approximation theory and numerical implementations.