This paper derives a two factor model for the term structure of interest rates that segments the yield curve in a natural way. The first factor involves modelling a non-negative short rate process that primarily determines the early part of the yield curve and is obtained as a truncated Gaussian...

The pricing and hedging of long dated derivative contracts is a challenging area of research. As a result of utility indifference pricing for general payoffs the growth optimal portfolio turns out to be the appropriate numeraire or benchmark with the real world probability measure as...

The objective of this paper is to consider defaultable term structure models in a general setting beyond standard risk-neutral models. Using as numeraire the growth optimal portfolio, defaultable interest rate derivatives are priced under the real-world probability measure. Therefore, the...

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...

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...

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 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...

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...