In continuous trading, ruin problems are important for several reasons. ln the first part of the paper a test criterion for bankruptcy is developed. In the present framework one implicitly assumes the investor's wealth to be different from zero, otherwise the model is not well-defined. It is of...

The problem of determining optimal portfolio rules is considered. Prices are allowed to be stochastic processes of a fairly general nature, expressible as stochastic integrals with respect to semimartingales. The set of stochastic differential equations assumed to describe the price behaviour...

We consider a situation where relative prices of assets may change continuously and also have discrete jumps at random time points. The problem is the one of portfolio optimization. If the utility function used is the logarithm, we first argue that an optimal investment plan exists. Secondly, we...

This paper develops several results in the modern theory of contingent claims valuation in a frictionless security market with continuous trading. The price model is a semi-martingale with a certain structure, making the return of the security a sum of an Ito-process and a random, marked point...