The main two areas of financial mathematics are portfolio optimization and option pricing. Portfolio optimization deals with the determination of the best investment strategy under certain constraints (e.g. risk, liquidity or budget constraints). Option pricing is concerned with valuation of derivative contracts with complex payoffs, dependent on tradable assets. The first part of the book deals with realistic problems of portfolio optimization. Thereby, the expected outcome of a utility function under constraints is maximised. For instance, the portfolio is optimized with fixed income and consumption constraints. The borrower rates of an investor depend on his debt-ratio, but usually they are assumed to be debt-independent. The author shows, how debt-ratio dependent borrower rates can be incorporated into portfolio optimization and how they affect the optimal trading strategy. In the second part of the book, some efficient methods to price Asian and average options are introduced. This book is adressed to quantitative researchers and portfolio managers in insurance companies and investment banks, as well as students of economics and financial mathematics.

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