Anderson (1976) was the first to give a non-standard construction of a Brownian motion. His approach was to use the binomial model in a discrete time with infinitesimal time steps. Pricing an option in a model similar to the Black-Scholes model with the nonstandard Brownian motion can be done by...

We examine the consumption and portfolio decisions of an agent with Friedman-Savage type period utility in continuous time. We find the Friedman-Savage consumer does not gamble, but will aggressively invest in risky activities for wealth levels that support a minimum subsistence level of...

Fund models are statistical descriptions of markets where all asset returns are spanned by the returns of a lower-dimensional collection of funds, modulo orthogonal noise. Equivalently, they may be characterised as models where the global growth-optimal portfolio only involves investment in the...