Stochastic

Many financial instruments have exhibited mean reversion, such as US and global equities [1], commodities [2], foreign exchange rates [3] as well as volatility indices [19]. Moreover, some researchers have also found mean reverting process to be very useful in modeling the interest rate and default risk dynamics [20]. In financial industry, some practitioners even attempt to profit by constructing mean-reverting prices which are usually known as statistical arbitrage or pair trading. Statistical

Stochastic Synchronization of micro grid energy resources operation in light of uncertainties B.Naveen1,B.Rajasekhar2,M.Guru Mahesh Reddy3 1.Student, Electrical and Electronics Engineering ,Gurunank Institute of Technical Campus, Hyderabad, India. 2. R&D Eng., Electrical and Electronics Engineering ,Deccan Enterprises Limited, Hyderabad, India. 3.Student, Electrical and Electronics Engineering ,Gurunank Institute of Technical Campus, Hyderabad, India. 1badarlanaveennani@gmail.com 2rajshaker

section{INTRODUCTION} The purpose of this paper will be to provide a brief survey of stochastic game methods in cyber security. The fast development of this area explains the abundance of literature and models. Due to our specific emphasis, and unintentional overlook, deserving references may not appear in this work. The main accent when describing the variety of theories will be on how to apply these models in a cyber-security set up. The focus will be on assisting in an approachable way the potential

Introduction to Martingale Theory Martingale Theory is a simple mathematical model which models sequence of a fair game [1]. It is a stochastic process on some probability space {Ω, F, P}. Originally it was used as a betting strategy during 18th century in France. In 1934, Paul Lévy introduced concept of Martingale in probability theory. It is named after ‘La Grande Martingale,’ which means strategy for even odd bets where bets are doubled every time we lose. Idea behind this betting strategy is

Abstract. This paper presents the cooperation between two searchers at the origin to seek for a random walk moving target on the line. Any information of the target position is not available to the searchers all the time. Rather than finding the conditions that make the expected value of the first meeting time between one of the searchers and the target is finite, we show the existence of the optimal search strategy which minimizes this first meeting time. The effectiveness of this model is illustrated

stochastic deterministic approach and attributes all deviations from the frontier to inefficiencies, a DEA-based estimate are sensitive to measurement errors or other noise in the data (Färe et al. 1994). Agricultural productivity and its determinants are important but have not always been well measured or well understood. Many previous estimates of productivity change have been computed using a growth accounting approach. The problem with this approach is that it makes overly restrictive assumptions

An additive noise is characteristic of almost all communication systems. This additive noise typically arises from thermal noise generated by random motion of electrons in the conductors comprising the receiver. In a communication system the thermal noise having the greatest effect on system performance is generated at and before the first stage of amplification. This point in a communication system is where the desired signal takes the lowest power level and consequently the thermal noise

SPECIFICATION OF THE MODEL GARCH (1, 1) MEAN EQUATION Sensex Returns = C1 + C2*CR+ e --------- (1.1) Nifty Fifty Returns = C1 + C2*CR+ e --------- (1.2) Sensex and Nifty Fifty returns – is the dependent variable and FTSE 100 is the independent variable VARIANCE EQUATION – THIS IS THE GARCH (1,1) MODEL Ht =C3 + C4 Ht-1 + C5*e2t-1 + C6*CR -------------- (1.2) Here, Ht= variance of the residual (error term) derived from equation 1.1 and 1.2 (current day’s variance or volatility of Index return)

Stochastic Calculus for Finance, Volume I and II by Yan Zeng Last updated: August 20, 2007 This is a solution manual for the two-volume textbook Stochastic calculus for finance, by Steven Shreve. If you have any comments or find any typos/errors, please email me at yz44@cornell.edu. The current version omits the following problems. Volume I: 1.5, 3.3, 3.4, 5.7; Volume II: 3.9, 7.1, 7.2, 7.5–7.9, 10.8, 10.9, 10.10. Acknowledgment I thank Hua Li (a graduate student at Brown University) for reading through

1. Introduction In 1973, Fischer Black, Myron Scholes and Robert Merton derived the Black-Scholes model of modelling derivatives prices for European stock options (Black & Scholes, 1973) and (Merton, 1973). This model has great importance on how traders determine the price and ways to hedge derivatives since the 1970’s (Hull, 2012), and led to other derivative instruments that have similar characteristics to option. Fundamentally, the Black-Scholes model make sure of a simple formula to determine