This article derives a series of analytic formulae for various contingent claims under the real-world probability measure using the stylised minimal market model (SMMM). This model provides realistic dynamics for the growth optimal portfolio (GOP) as a well-diversified equity index. It captures...

This paper studies a class of one-factor local volatility function models for stock indices under a benckmark approach. It assumes that the dynamics for a large diversified index approximates that of the growth optimal portfolio. The pricing and hedging of derivatives under the benchmark...

This paper identifies a distribution, which fits the daily log-returns of index benchmarked share prices. For this data the Student t distribution appears to provide the best fit under the maximum likelihood ratio test within the class of symmetric generalised hyperbolic distributions. A share...

This paper considers a modified constant elasticity of variance (MCEV) model. This model uses the familiar constant elasticity of variance form for the volatility of the growth optimal portfolio (GOP) in a continuous market. It leads to a GOP that follows the power of a time-transformed squared...

This paper constructs and compares various total return world stock indices based on daily data. Due to diversification these indices are noticeably similar. A diversification theorem identifies any diversified portfolio as a proxy for the growth optimal portfolio. The paper constructs a...

This paper aims to discuss the optimal selection of investments for the short and long run in a continuous time financial market setting. First it documents the almost sure pathwise long run outperformance of all positive portfolios by the growth optimal portfolio. Secondly it assumes that every...

This paper describes a two-factor model for a diversified market index using the growth optimal portfolio with a stochastic and possibly correlated intrinsic time scale. The index is modeled using a time transformed squared Bessel process of dimension four with a lognormal scaling factor for the...

This paper proposes a unified framework for portfolio optimization, derivative pricing, modeling and risk measurement in financial markets with security price processes that exhibit intensity based jumps. It is based on the natural assumption that investors prefer more for less, in the sense...

This paper considers a market containing both continuous and discrete noise. Modest assumptions ensure the existence of a growth optimal portfolio. Non-negative self-financing trading strategies, when benchmarked by this portfolio, are local martingales under the real-world measure. This...

We extend the credit risk valuation framework introduced by Gatfaoui (2003) to stochastic volatility models. We state a general setting for valuing risky debt in the light of systematic risk and idiosyncratic risk, which are known to affect each risky asset in the financial market. The option...