In finance and economics the key dynamics are often specified via stochastic differential equations (SDEs) of jump-diffusion type. The class of jump-diffusion SDEs that admits explicit solutions is rather limited. Consequently, discrete time approximations are required. In this paper we give a...

The paper describes a consistent, integrated framework for modeling and pricing in finance, insurance and other areas of risk management. The growth optimal portfolio is taken as a benchmark. In the resulting price system expected future benchmarked, nonnegative prices are not greater that the...

In this paper we identify distributions which suitably fit log-returns of the world stock index (WSI) when these are expressed in units of different currencies. By searching for a best fit in the class of symmetric generalized hyperbolic distributions the maximum likelihood estimates appear to...

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 proposes a financial market model that generates stochastic volatilities and stochastic interest rates using a minimal number of factors that characterise the dynamics of different denominations of a benchmark portfolio. It models asset prices essentially as functionals of square root...

This paper introduces a general market modeling framework under which the Law of One Price no longer holds. A contingent claim can have in this setting several self-financing, replicating portfolios. The new Law of the Minimal Price identifies the lowest replicating price process for a given...

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...