Continuous Time Analysis of Fleeting Discrete Price Moves

Discrete Time vs Continuous Time Stock-price Dynamics and implications for Option Pricing

In the present paper we construct stock price processes with the same marginal lognormal law as that of a geometric Brownian motion and also with the same transition density (and returns’ distributions) between any two instants in a given discrete-time grid. We then illustrate how option prices based on such processes differ from Black and Scholes’, in that option prices can be either arbitrari...

Discrete analysis of continuous behaviour in real-time concurrent systems

This thesis concerns the relationship between continuous and discrete modelling paradigms for timed concurrent systems, and the exploitation of this relationship towards applications, in particular model checking. The framework we have chosen is Reed and Roscoe’s process algebra Timed CSP, in which semantic issues can be examined from both a denotational and an operational perspective. The cont...

Discrete Event, Continuous Time RNNs

We investigate recurrent neural network architectures for event-sequence processing. Event sequences, characterized by discrete observations stamped with continuous-valued times of occurrence, are challenging due to the potentially wide dynamic range of relevant time scales as well as interactions between time scales. We describe four forms of inductive bias that should benefit architectures fo...

Discrete-time Equivalents to Continuous-time Systems

Continuous-time consensus with discrete-time communications

This paper addresses the problem of reaching consensus among a group of agents that evolve in continuous-time and exchange information at discretetime instants, referred to as update times. Each agent has its own sequence of update times and therefore the agents are not required to keep synchronized clocks among them. At each update time, an agent receives from a subset of the other agents thei...