Refik Güllü

An introduction to stochastic models in financial decision making. Discrete time models: Martingales, risk-neutral probability measure and Radon-Nikodym derivative in discrete time. Brownian motion, Ito’s formula and change of measure in continuous time, along with the Black-Scholes model. Discussion on stopping times and their application to American options. Stochastic models for interest rates and fixed income derivatives.

Exploring data patterns; moving averages, simple and double exponential smoothing, smoothing methods with seasonal data, Holt-Winter method; simple and multiple regression; regression with time series data; ARIMA models; Box-Jenkins method for forecasting; demand management and applications.

Description and characteristics of inventory models; economic order quantity and economic lot size models; multiple product and multiple location models under deterministic demand; stochastic single-item models with capacity constraints and lead-times; structure of dynamic inventory policies; multi-item stochastic demand inventory models; supply chain models and current issues in inventory planning.

Basic topics in probability theory; sample space, probability, and conditional probability; random variables, marginal, joint and conditional distributions; expectations and conditional expectations; hypergeometric, binomial, geometric distributions and their implications in IE/OR; Poisson, exponential, Erlang, gamma distributions and the Poisson arrival model; moment generating functions and Laplace transforms; law of large numbers, central limit theorem, and the Normal distribution; numerical and computational aspects of random variable generation.