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 proposes a consistent benchmark approach to price weather derivatives. The growth optimal portfolio to price weather derivatives. The growth optimal portfolio is used as numeraire such that all benchmarked fair price processes are martingales. No measure transformation is needed for...

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 describes a two-factor model for a diversifed index that attempts to explain both the leverage effect and the implied volatility skews that are characteristic of index options. Our formulation is based on an analysis of the growth optimal portfolio and a corresponding random market...

The paper discusses various roles that the growth optimal portfolio (GOP) plays in finance. For the case of a continuous market we showhow the GOP can be interpreted as a fundamental building block in financial market modeling, portfolio optimization, contingent claim pricing and risk...

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 proposes an integrated appraoch to discrete time modelling in finance and insurance. This approach is based on the existence of a specific benchmark portfolio, known as the growth optimal portfolio. When used as numeraire, this portfolio ensures that all benchmarked price processes...

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 proposes analternative approach to the modeling of the interest rate term structure. It suggests that the total market price for risk is an important factor that has to be modeled carefully. The growth optimal portfolio, which is characterized by this factor, is used as refernce unit...