Fake Geometric Brownian Motion And Its Option Pricing

In this thesis, we begin with introducing the notion of a fake geometric Brownian motion in analogy to the fake Brownian motion. Secondly we construct two discontinuous fake geometric Brownian motion processes via the solutions to the Skorokhod embedding problem. Finally we simulate European and path-dependent option pricings for stock prices following these processes, to see how different the results can be compared with the traditional Black & Scholes setting.\ud \ud Key words: fake Brownian motion, fake geometric Brownian motion, Skorokhod embedding problem, Azema-Yor solution, reversed Azema-Yor solution

An Architecture for Distributed Energies Trading in Byzantine-Based Blockchain

With the development of smart cities, not only are all corners of the city connected to each other, but also connected from city to city. They form a large distributed network together, which can facilitate the integration of distributed energy station (DES) and corresponding smart aggregators. Nevertheless, because of potential security and privacy protection arisen from trustless energies trading, how to make such energies trading goes smoothly is a tricky challenge. In this paper, we propose a blockchain-based multiple energies trading (B-MET) system for secure and efficient energies trading by executing a smart contract we design. Because energies trading requires the blockchain in B-MET system to have high throughput and low latency, we design a new byzantine-based consensus mechanism (BCM) based on node's credit to improve efficiency for the consortium blockchain under the B-MET system. Then, we take combined heat and power (CHP) system as a typical example that provides distributed energies. We quantify their utilities, and model the interactions between aggregators and DESs in a smart city by a novel multi-leader multi-follower Stackelberg game. It is analyzed and solved by reaching Nash equilibrium between aggregators, which reflects the competition between aggregators to purchase energies from DESs. In the end, we conduct plenty of numerical simulations to evaluate and verify our proposed model and algorithms, which demonstrate their correctness and efficiency completely

Decentralized Narrowband and Wideband Spectrum Sensing with Correlated Observations

This dissertation evaluates the utility of several approaches to the design of good distributed sensing systems for both narrowband and wideband spectrum sensing problems with correlated sensor observations