Synopsis for Optimization Methods in Finance

Further details (Dr Raphael Hauser - 12 lectures - TT - Option course)

Overview

Second order cone programming (SOCP) is a class of optimization problems that occur naturally throughout mathematical finance, particularly in
quantitative risk management, in specifying the size of trades in algorithmic trading, in handling transaction costs and parameter uncertainty, and
in model calibration. Participants of this course learn the wide spectrum of SOCP applications through a series of example models that are of direct
practical relevance, and they learn some aspects of the underlying theory that are important to the user of state-of-the art software for solving such problems.

Synopsis

[(1)] Optimization terminology, classfication of problems, optimality conditions.

[(2)] Conic programming modelling. Mean-variance optimization.

[(3)] Rebalancing a portfolio with sesquilinear transaction costs.

[(4)] A multiperiod investment model with linear transaction costs.

[(5)] A high frequency trading strategy.

[(6)]An optimization approach to optimal execution strategies.

[(7)] Newton's method.

[(8)] Convex duality.

[(9)] The barrier method for convex programming. 
 
[(10)] Coherent risk measures.

[(11)] Using tail risk measures in optimization models.

[(12)] Robust portfolio optimization.