When simulating discrete time approximations of solutions of stochastic differential equations (SDEs), numerical stability is clearly more important than numerical efficiency or some higher order of convergence. Discrete time approximations of solutions of SDEs are widely used in simulations in...

This paper describes a financial market modelling framework that exploits the notion of a deflator. The demonstrations of the deflator measured in units of primary assets form a minimal set of basic financial quantities that completely specify overall market dynamics. Risk premia of asset prices...

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 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 considers the continuous time pricing and hedging of European options in the presence of small transaction costs and frequent trading under local risk minimisation. The approach yields mean-self-financing strategies. The resulting dynamical hedges adapt the trading frequency in...

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...

The paper describes a continuous time share market model with a minimal number of factors. These factors are powers of Bessel processes. The asset prices are formed by ratios of the factors and have consequently leptokurtic return distributions. In this framework stochastic volatility with...

A financial market model with general semimartingale asset-price processes and where agents can only trade using no-short-sale strategies is considered. We show that wealth processes using continuous trading can be approximated very closely by wealth processes using simple combinations of...

This paper extends the benchmark framework of Platen (2002) by introducing a sequence of incomplete markets, having uncertainty driven by a Wiener process and a marked point process. By introducing an idealized market, in which all relevant economical variables are observed, but may not all be...

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...