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...

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...