We suggest the method of evaluation of illiquid assets on the market in the presence of proportional transaction costs by using two consumption/investment models. We study an investor's implicit evaluation of an illiquid asset whose trading incurs a proportional transaction cost. We show that...

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...

We study an investor¡¯s decision to switch from active portfolio management to passive management. This problem is mathematically modelled by a mixture of a consumption-portfolio selection problem and an optimal stopping problem. We assume that the investor has stochastic differential utility...

We consider a consumption and investment problem where an investor¡¯s investment opportunity gets enlarged when she becomes rich enough, i.e., when her wealth touches a critical level. We derive optimal consumption and investment rules assuming that the investor has a time-separable von...