Portfolio Optimization and Option Pricing: Selected Problems and Efficient Methods

The main two areas of financial mathematics areportfolio optimization and option pricing. Portfoliooptimization deals with the determination of the bestinvestment strategy under certain constraints (e.g.risk, liquidity or budget constraints). Optionpricing is concerned with valuation of derivativecontracts with complex payoffs, dependent on tradableassets. The first part of the book deals with realisticproblems of portfolio optimization. Thereby, theexpected outcome of a utility function underconstraints is maximised. For instance, the portfoliois optimized with fixed income and consumptionconstraints. The borrower rates of an investor dependon his debt-ratio, but usually they are assumed to bedebt-independent. The author shows, how debt-ratiodependent borrower rates can be incorporated intoportfolio optimization and how they affect theoptimal trading strategy. In the second part of thebook, some efficient methods to price Asian andaverage options are introduced. This book is adressed to quantitative researchers andportfolio managers in insurance companies andinvestment banks, as well as students of economicsand financial mathematics.