On stochastic calculus related to financial assets without semimartingales
نویسندگان
چکیده
منابع مشابه
No Arbitrage without Semimartingales
We show that with suitable restrictions on allowable trading strategies, one has no arbitrage in settings where the traditional theory would admit arbitrage possibilities. In particular, price processes that are not semimartingales are possible in our setting, for example fractional Brownian motion.
متن کاملAnticipative Stochastic Calculus with Applications to Financial Markets
In this thesis, we study both local time and Malliavin calculus and their application to stochastic calculus and finance. In the first part, we analyze three aspects of applications of local time. We first focus on the existence of the generalized covariation process and give an approximation when it exists. Thereafter, we study the decomposition of ranked semimartingales. Lastly, we investigat...
متن کاملIeor E4707: Financial Engineering: Continuous-time Models Introduction to Stochastic Calculus 1 Martingales and Brownian Motion Introduction to Stochastic Calculus 2 Quadratic Variation Introduction to Stochastic Calculus 3 Stochastic Integrals Introduction to Stochastic Calculus
These notes provide an introduction to stochastic calculus, the branch of mathematics that is most identified with financial engineering and mathematical finance. We will ignore most of the “technical” details and take an “engineering” approach to the subject. We will cover more material than is strictly necessary for this course. Any material that is not required, however, should be of value f...
متن کاملAn introduction to stochastic integration with respect to continuous semimartingales
Contents Preface v 1 Continuous-time stochastic processes 1 1.1 Measurability and stopping times. . Bibliography 133 iv CONTENTS Preface This monograph concerns itself with the theory of continuous-time martingales with continuous paths and the theory of stochastic integration with respect to continuous semimartingales. To set the scene for the theory to be developed, we consider an example. As...
متن کاملExponential Stability for Stochastic Differential Equations with Respect to Semimartingales
Consider a stochastic differential equation with respect to semimartingales dX(t)=AX(f)dp(t)+G(X(t),r)dM(r) which might be regarded as a stochastic perturbed system of dX(t)=AX(t)d/L(t). Suppose the second equation is exponentially stable almost surely. What we are interested in in this paper is to discuss the sufficient conditions under which the first equation is still exponentially stable al...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin des Sciences Mathématiques
سال: 2011
ISSN: 0007-4497
DOI: 10.1016/j.bulsci.2011.06.008