Abstracts

There is an increasing literature on models and phenomena that cannot be fitted under the classical no-arbitrage paradigm. The benchmark approach provides a generalized framework for a unified treatment of such models and phenomena in portfolio optimization, derivative pricing, financial planning, insurance, pensions and risk measurement. It extends in a constructive manner the classical theory and, thus, provides access to a more realistic modelling world. Its central building block is the numeraire portfolio, the benchmark and numeraire, for which surprisingly well performing proxies can be constructed. Nonnegative benchmarked price processes form supermartingales, possibly with negative drifts. Maximum drawdown constrained portfolios will balance long term growth and maximum drawdowns. A highly tractable two component diffusion model for well-diversified equity portfolios will be conjectured and empirically studied. The real world pricing formula emerges for the valuation of competitive prices. More expensive pricing rules are permitted with benchmarked prices that form supermartingales. Benchmarked risk minimization minimizes for not fully hedgeable claims the price and the fluctuations of the benchmarked profit and loss. Examples of extreme maturity pension contracts demonstrate significant savings when valued and hedged accordingly.