This paper derives a unified framework for portfolio optimization, derivative pricing, financial modeling and risk measurement. It is based on the natural assumption that investors prefer more or less, in the sense that the higher drift is preferred. Each such investor is shown to hold an...

This paper considers a class of incomplete financial market models with security price processes that exhibit intensity based jumps. The benchmark or numeraire is chosen to be the growth optimal portfolio. Portfolio values, when expressed in units of the benchmark, are local martingales. In...

This paper considers a modification of the well-known constant elasticity of variance model where it is used to model the growth optimal portfolio. It is shown taht, for this application, there is no equivalent risk neutral pricing methodology fails. However, a consistent pricing and hedging...

This paper considers diversified portfolios in a benchmark framework. A new limit theorem for the approximation of the benchmark, which is the growth optimal portfolio, is obtained. In a diverse market it is shown that there exist approximations for the benchmark that are independent of model...

The paper describes a general framework for contingent claim valuation for finance, insurance and general risk management. It considers security prices and portfolios with finite expected returns, where the growth optimal portfolio is taken as numeraire or benchmark. Benchmarked nonnegative...

This paper introduces a benchmark model for financial markets, which is based on the unique characterization of a benchmark portfolio that is chosen to be the growth optimal portfolio. The general structure of risk premia for asset prices as an average of appreciation rates. The benchmark model...

This paper considers a diversified world stock index in a continuous financial market with the growth optimal portfolio (GOP) as the reference unit or benchmark. Diversified broadly based portfolios, which include major world stock market indices, are shown to approximate the GOP. It is...

This paper proposes a class of financial market models with security price processes that exhibit intensity based jumps. Primary security account prices, when expressed in units of the benchmark, turn out to be local martingales. The benchmark model exludes, so called, benchmark arbitrage but...

This paper considers diversifed portfolios in a sequence of jump diffusion market models. Conditions for the approximation of the growth optimal portfolio (GOP) by diversified portfolios are provided. Under realistic assumptions, it is shown that diversified portfolios approximate the GOP...

The paper presents a consistent approach to the modeling of general and specific market risk as defined in regulatory documents. It compares the statistically based beta-factor model with a class of benckmark models that use a broadly based index as major building block for modeling. The...