In this paper we provide conditions under which a preference relation can be represented by concave utility functions … preference relations by continuous and weakly increasing utility functions due to Wold (1943). For continuous and homothetic … concave utility function is also a necessary condition for such a numerical representation. In fact we are able to obtain a …

class of extensions which involves an arbitrary function. Similar results are obtained for utility functions that represent …

In this paper, we apply stochastic maximum principles to derive representations for exponential utility indifference … prices. We also obtain the related optimal portfolio processes and utility indifference hedging strategies. To illustrate our … theoretical results, we present several concrete examples and study the limit behavior of utility indifference prices for …